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STA301 IMP notes Headings andSome Questions AnswersPrepared by……………. mePie Chart : Pie Chart consists of a circle which is divided into two or more mars inaccordance with the number of distinct classes that we have in our data.StatisticalInference :Statistical Inference is an estimate or prediction or some othergeneralization about a Population based on information contained in asample.Statistics : Statistics is that science which enables to draw conclustions about variousphenomena one the basis of real data collected on sample basis.Sample : Sample is that part of the Population from which information is collected.What ismeant byorder?. :Order: Arrangement of objects in ascending or descending way is knownas order.Population:The collection of all individuals,items or data under consideration instatistical study is called Population.NominalScale :The classification or grouping of observatoins into mutually exclusivequalitative categories is said to constitute a nominal scale e.g students areclassified as male and female.OrdinalScale :It includes the characteristic of a nominal scale and in addition has theproperty of ordering or ranking of measurments e.g the performance ofstudents can be rated as excellent,good or poor.IntervalScale :A measurment scale possessing a constant interval size but not true zeropoint is called an Interval Scale.Ratio Scale:It is a special kind of an interval scale in which the scale of measurmenthas a true zero point as its origin.Median : Median of a set of values arranged in ascending or descending order ofmagnitude is defined as middle value if the number of values is odd andmean of two middle values if the number of values is even.Median is avalue at or below which 50% of data lie.Average : A single value which intended to represent a distribution or a set of dataGenerated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.

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as a whole is called an average. It is more or less a central value aroundwhich the observations tend to cluster so it is called measure of centraltendency. Since measure of central tendency indicate the location of thedistribution on X axis so it is also called measure of location.MeanDeviation :The mean deviation is defined as the arithmetic mean of the deviationsmeasured either from the mean or from the median, all deviations beingcounted as positive.Chebshev'sTheorm :Chebshev's Theorem states that "For any number K greater than one atleast 1-1/k2 of the data values fall with in K standard deviations of themean i.e. within the interval.Moments : Moments are the arithmetic means of the powers to which the deviationsare raised.Kurtosis : kurtosis is the degree of peakness of a distribution usually taken relativeto a normal distribution.Correlation:Correlation is a measure of the strength or the degree of relationshipbetween two random variables. OR Interdependence of two variables iscalled correlation.VennDiagram :A diagram that is understood to represent sets by circular regions, parts ofcircular regions or their complements with respect to a rectanglerepresenting the space S is called a Venn diagram. The Venn diagramsare used to represent sets and subsets in a pictorial way and to verify therelationship among sets and subsets.MutuallyExclusiveEvent :Two events are said to be mutually exclusive events if and only if theycan not both occur together at the same time. OR Two events are said tobe mutually exclusive events if the occurrence of one event discard theoccurrence of other event.Independentevents :Two events A and B in the same sample space S, are defined to beindependent (or statistically independent) if the probability that one eventoccurs, is not affected by whether the other event has or has not occured.Randomvariable :A numerical quantity whose value is determined by the outcome of arandom experiment is called a random variable.DistributionFunction :

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The function which gives the probability of the event that X takes a valueless than or equal TO a specified value x is called a distribution functionand is also called the cumulative distribution function.Cumulative The function which gives the probability of the event that X takes a valueGenerated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.DistributionFunction :less than or equal TO a specified value x is called a cumulativedistribution function and is also called the distribution function.SamplingFrame :A sampling frame is a complete list of all the elements in the population.SamplingError :The sampling error is the difference between the the sample statistic andthe population parameter.ProbabilitySamples :Probability samples are those in which following the sampling plan eachunit in the poplation has a known probability of being included in thesample.Nonprobabilitysamples :Non probability samples are those in which the sample elements are thearbitrarily selected by the sampler because in this judgment the elementsthus chosen will most effectively represent the Population.FrequencyPolygon :A frequency polygon is obtained by plotting the class frequencies againstthe mid-points of the classes, and connecting the points so obtained bystraight line segments.Variable : A measurable quantity which can vary from one individual or object toanother is called a variable.Constant : A quantity which can assume only one value is called a constantEvent. : the possible outcomes of an experiment is known as event.Data. : A well defined collection of objects is known as data.Mode : The mode is a value which occures most frequently in a set of data i.e. itindicates the most common resultBox andWhiskerplot :A Box and Whisker plot provides a graphical representation of datathrough its five number summary.The fivenumbersummary :

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A five number summary consists of X0, Q1, median, Q3, and Xm. Itenables us to find the shape of the distribution without drawing a graph.EXHAUSTIVEEVENTS :Two or more than two mutually exclusive events are said to beexhaustive events when their union constitute the entire sample spaceEqually Two events A and B are said to be equally likely when one event is asGenerated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.likelyevents :likely to occur as otherProbability:Probability is defined as the ratio of favorable cases over equally likelycases.Table : Table is a systematic arrangement of data into vertical columns andhorizontal rows.Tabulation:The process of arranging data into rows and columns is called tabulation.Classification:The process of arranging data in classes or categories according tosome common characteristics present in the data is called classification.Class Markor MidPoint :The class mark or mid point is that value which divides a class into twoequall parts.Mid Poinor ClassMark :The mid point or class mark is that value which divides a class into twoequal parts.Measure oflocation :A single value which intended to represent a distribution or a set of dataas a whole is called an average. It is more or less a central value aroundwhich the observations tend to cluster so it is called measure of centraltendency. Since measure of central tendency indicate the location of thedistribution on X axis so it is also called measure of location.The SemiinterquartileRange :The quartile deviation or the Semi-interquartile Range is defined as halfof the difference between the first and third quartiles.Thecoefficient

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of variation:The coefficient of variation expresses the standard deviation as thepercentage of the arithmetic mean.DisjointSet :Two sets A and B are said to be disjoint Sets if they have no elements incommon.DISTRIBUTIONFUNCTION: :The distribution function of a random variable X, denoted by F(x),is defined by F(x) = P(X < x). The function F(x) gives theprobability of the event that X takes a value LESS THAN OREQUAL TO a specified value x. The distribution function isabbreviated to d.f. and is also called the cumulative distributionGenerated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.function (cdf) as it is the cumulative probability function of therandom variable X from the smallest value up to a specific value x.Experimentaldesign: :An experimental design is a set of rules or a plan to collect the datarelevant to the problem under investigation in such a way as to providethe basis for valid and objective inferences about the stated problem.The plan usually consists of collection of the treatments, specificationof experimental layout, allocation of treatments.ExperimentalUnit: :An experimental unit is the basic unit to which the experiment isperformed. It is the basic unit to which the treatment is applied and inwhich the variable under investigation is measured and analyzed.RandomizedDeigns; :These designs are those in which treatments are applied to experimentalunits randomly and conclusions are supported by the statistical results.BasicRandomizedDesigns: :Randomization Replication Local ControlRandomization::It is a random process of assigning treatments to the experimentalunit. The random process implies that every possible allocation oftreatments has the same probability.Replication::The second principle of an experimental design is replication which isthe repetition of the basic experiment. It is a complete run of all the

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treatments to be tested in the experiment.LocalControl: :It is used to bring all extraneous sources of variations under control. Forthis purpose we use Local Control, a term referring to the amount ofbalancing, blocking and grouping of the experimental units.CompleteRandomizedDesigns :In this design treatments are applied to the experimental unitscompletely at random, that is randomization is done without anyrestrictions. Design is completely flexible, any number of treatments andany number of units per treatments can be applied.ANOVA : Analysis of variance is defined as the procedure by means of which thetotal variability of the set of data measured by total sum of square ispartitioned into components that measure different sources of variations.The procedure thus permits the decomposition of the total SS into to thecomponent SS which are corresponding to the real and suspected sourcesof variations.RandomizedcompleteRandomized complete block Design (RCB) is a design in which •Experimental material is divided into groups or blocks in such a mannerGenerated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.blockDesign(RCB): :that experimental units within a particular block are relativelyhomogeneous. • Each block contains complete set of treatments i.e. itconstitutes a replication of treatments. • Treatments are assigned atrandom to the experimental units with in each block which means therandomization is restricted with blocks.LatinSquareDesign: :LS design is an arrangement of k treatments in a k*k square, where thetreatments are grouped in blocks in two directions, the direction beingorthogonal to each other and to the treatments, and where the treatmentsappear once and only once in each in each direction. It should be notedthat in Latin square design, the number of rows, the number of columnsand number of treatments must be equalCriticalValue :The value that separates the critical region from the acceptance region, iscalled the critical value(s).Level ofsignificance

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:Level of significance of a test is the probability used as a standard forrejecting null hypothesis Ho when Ho is assumed to be true. The level ofsignificance acts as a basis for determining the critical region of the test.statistics 2:Statistics is a science of facts and figures.Deciles : Deciles are those nine quantities that divide the distribution into tenequall parts.Percentiles:Percentiles are those ninety nine quantities that divide the distributioninto hundred equall partsArithmeticMean :Arithmetic Mean is a value obtained by dividing the sum of theobservations by their numbers.GeometricMean :The Geometric Mean G, of a set of n positive values is defined as thepositive nth root of their product.AbsoluteMeasure ofDispersion:An absolute measure of dispersion is one that measures the dispersion interms of the same units, or in the square of units as the units of the data.Dispersion:The variability that exists between data set.RelativeMeasure ofDispersionA Relative Measure of Dispersion is one that measures the dispersion interms of a ratio, coefficient or percentage and is independent of the unitsof measurement.Generated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.:Range : The range is defined as the difference between the maximum andminimum values of a data set.QuartileDeviation :The quartile deviation is defined as half of the difference between thefirst and third quartiles.Set : A set is any well defined collection or list of distinct objects.standarderror of

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estimate :The degree of scatter of the observed values about the regression linemeasured by what is called standard deviation of regression or standarderror of estimate.Class ofSets :A set of sets is called a class.PrimaryData :The data published or used by an organization which originally collectedthem are called primary data thus the primary data are thr first handinformation collected, complied, and published by an organization for acertain purpose.SecondaryData :The data published or used by an organization other than the one whichorigninally collected them are known as secondary data.HarmonicMean :Harmonic mean is defined as the reciprocal of the arithmetic mean of thereciprocals of the values.Quartiles : Quartiles are those three quantities that divide the distribution into fourequal parts.Quantiles : Collectively the quartiles, the deciles,percentiles and other valuesobtained by equall sub-division of the data are called quantiles.IndexNumber :An Index Number is a statistical measure which shows changes in avariable or group of related variables with respect to time, geographiclocation or other characteristics such as income, profession etc.StandardDeviation :Standard Deviation is defined as the positive square root of the mean ofthe squared deviations of the values from their mean.Variance : Variance is defined as the square of the standard deviation.Regression:Dependence of one variable on the other variable is called regression. OREstimation or prediction of one variable on the basis of other variable isGenerated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.called regression.RandomExperiment:An experiment which produces different results even though it is repeateda large number of times under essentially similar conditions is called arandom experiment.

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Sub Set : A set that consists of some elements of an other set is called a subset ofthat set.Non-SamplingError :Such errors which are not attributable to sampling but arise in the processof data collection even if a complete count is carried out.Skewness : Skewness is the lack of symmetry in a distribution around some centralvalue (mean,median or mode).It is thus the degree of a symmetry.Permutation:an arrangement of all or some of a set of objects in a definite order iscalled permutation.UniversalSet :All sets are subsets of one particular set called universal set.SampleSpace :The set or collection of all possible outcomes of an experiment is calledthe sample space.ConditionalProbability:The probability of the occurence of an event A when it is known thatsome other event B has already occured is called the conditionalprobability.Degrees offreedom :Degrees of freedom can be defined as the number of observations in thesample minus the number of population parameters that are estimatedfrom the sample data (from those observationsP value : The p-value is a property of the data, and it indicates “how improbable”the obtained result really is.TestStatistic :A statistic (i.e. a function of sample data not containing any parameter),which provides a basis for testing a null hypothesis, is called a teststatistics.Additionlaw :A probability law used to compute the probability of a union of twoevents, denoted A and B. It is P(AÈB)=P(A)+P(B)-P(AÇB). For mutuallyexclusive events, because P(AÇB)=0, it reduces to P(AÈB)=P(A)+P(B).AlternativehypothesisThe hypothesis concluded to be true if the null hypothesis is rejected.Generated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.

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:ANOVAtable :A table used to summarize the analysis of variance computations andresults. It contains columns showing the source of variation, the sum ofsquares, the degrees of freedom, the mean square, and the F values.Bayes'theorem :A method used to compute posterior probabilities.Binomialprobabilitydistribution:A probability distribution showing the probability of x successes in ntrials of a binomial experiment.Binomialprobabilityfunction :The function used to compute probabilities in a binomial experiment.Blocking : The process of using the same or similar experimental units for alltreatments. The purpose of blocking is to remove a source of variationfrom the error term and hence provide a more powerful test for adifference in population or treatment means.Box plot : A graphical summary of data. A box, drawn from the first to the thirdquartiles, shows the location of the middle 50% of the data. Dashed lines,called whiskers, extending from the ends of the box show the location ofdata values greater than the third quartile and data values less than thefirst quartile. The locations of any outliers are also noted.Centrallimittheorem :A theorem that enables one to use the normal probability distribution toapproximate the sampling distribution of the sample mean and sampleproportion whenever the sample size is large.Consistency:A property of a point estimator that is present whenever larger samplesizes tend to provide point estimates closer to the population parameterHistogram:A graphical presentation of a frequency distribution, relative frequencydistribution, or percent frequency distribution of quantitative dataconstructed by placing the class intervals on the horizontal axis and thefrequencies on the vertical axis.Nullhypothesis:The hypothesis tentatively assumed true in the hypothesis testing

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procedure. or A null hypothesis, generally denoted by the symbol H0, isany hypothesis which is to be tested for possible rejection or nullificationunder the assumption that it is true.Generated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Normalprobabilitydistribution:A continuous probability distribution. Its probability density function isbell shaped and determined by its mean m and standard deviation s.Observation:The set of measurements obtained for a single element.Ogive : A graph of a cumulative distribution.One-tailedtest :A hypothesis test in which rejection of the null hypothesis occurs forvalues of the test statistic in one tail of the sampling distribution. or Theentire rejection region lies in only one of the two tails, either in the righttail or in the left tai, of the sampling distribution of the test-statistic, iscalled a one-tailed test or one-sided test.Parameter : numerical characteristic of a population, such as a population mean, apopulation standard deviation, a population proportion, and so on.Pointestimate :A single numerical value used as an estimate of a population parameter.Pointestimator :The sample statistic that provides the point estimate of the populationparameter.Poissonprobabilitydistribution:A probability distribution showing the probability of x occurrences of anevent over a specified interval of time or space.Poissonprobabilityfunction :The function used to compute Poisson probabilities.Populationparameter :A numerical value used as a summary measure for a population of data(e.g., the population mean, the population variance, and the populationstandard deviation).Posteriorprobabilities

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:Revised probabilities of events based on additional information.Powercurve :A graph of the probability of rejecting H0 for all possible values of thepopulation parameter not satisfying the null hypothesis. The power curveprovides the probability of correctly rejecting the null hypothesis.Generated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Power : The probability of correctly rejecting H0 when it is false.Probabilitydensityfunction :A function used to compute probabilities for a continuous randomvariable. The area under the graph of a probability density function overan interval represents probability.Probabilityfunction :A function, denoted by f(x), that provides the probability that x assumes aparticular value for a discrete random variable.Qualitativedata :Data that are labels or names used to identify an attribute of eachelement. Qualitative data may be nonnumeric or numeric.Qualitativevariable :A variable with qualitative data.Quantitativedata :Data that indicate how much or how many of something. Quantitativedata are always numeric.tDistribution:A family of probability distributions that can be used to develop intervalestimates of a population mean whenever the population standarddeviation is unknown and the population has a normal or near-normalprobability distribution.Targetpopulation:The population about which inferences are made.Treatment : Different levels of a factor.Treediagram :A graphical representation helpful in identifying the sample points of anexperiment involving multiple steps.Two-tailed

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test :A hypothesis test in which rejection of the null hypothesis occurs forvalues of the test statistic in either tail of the sampling distribution.Type Ierror :The error of rejecting H0 when it is true.Type IIerror - :The error of accepting H0 when it is false.Unbiasedness:A property of a point estimator when the expected value of the pointestimator is equal to the population parameter it estimates.Union of The event containing all sample points that are in A, in B, or in both. TheGenerated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.events Aand B :union is denoted AÈB.Types ofExperimentalDesigns: :Systematic Designs Randomized designSystematicDesigns: :These designs are those in which treatments are applied to theexperimental units by some systematic manner that is choice of theexperimenterAcceptanceandrejectionregion: :All possible values which a test-statistic may assume can be divided intotwo mutually exclusive groups: One group consisting of values whichappear to be consistent with the null hypothesis (i.e. values which appearto support the null hypothesis), and the other having values which lead tothe rejection of the null hypothesis. The first group is called theacceptance region and the second set of values is known as the rejectionregion for a testType Ierror: :When we perform a hypothesis test, we derive evidence from the samplein the form of a test statistics. There is a possibility that sample may leadus to make a wrong decision. We may reject the hypothesis when it is infact true. This type of error is called an error of first kind or type I-error.The probability of committing a type I error is denoted by α. Thus α is theprobability of rejecting null hypothesis Ho when Ho true.Type II

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error: :When we perform a hypothesis test, we derive evidence from the samplein the form of a test statistics. There is a possibility that sample may leadus to make a wrong decision. We may accept the hypothesis when it is infact false. This type of error is called an error of second kind or a Type IIerror. The probability of committing a type II error is denoted by β. Thusβ is the probability of accepting null hypothesis Ho when Ho false.Classmidpoint :The point in each class that is halfway between the lower and upper classlimits.Complementof event A :The event consisting of all sample points that are not in A.Dependentvariable :The variable that is being predicted or explained. It is denoted by y.Descriptivestatistics :Tabular, graphical, and numerical methods used to summarize data.Dot plot : A simple graphical summary of data with each observation representedGenerated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.by a dot placed above a horizontal axis that shows the range of values forthe observations.Discreterandomvariable :A random variable that may assume either a finite number of values or aninfinite sequence of values.Empiricalrule :A rule that states the percentages of items that are within one, two, andthree standard deviations from the mean for mound-shaped, or bellshaped,distributions.Experiment:A process that generates well-defined outcomes.Binomialexperiment:A probability experiment having the following four properties: consists ofn identical trials, two outcomes (success and failure) are possible on eachtrial, probability of success does not change from trial to trail, and thetrials are independent.Factorialexperiment:

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An experimental design that allows statistical conclusions about two ormore factors.Fivenumbersummary :An exploratory data analysis technique that uses the following fivenumbers to summarize the data set: smallest value, first quartile, median,third quartile, and largest value.Frame : A list of the sampling units for a study. The sample is drawn by selectingunits from the frame.Frequencydistribution:A tabular summary of data showing the number (or frequency) of itemsin each of several non-overlapping classes.Groupeddata :Data available in class intervals as summarized by a frequencydistribution. Individual values of the original data are not available.Independentvariable :The variable that is doing the predicting or explaining. It is denoted by x.Intersectionof A and B:The event containing all sample points that are in both A and B. Theintersection is denoted AÇB.JointprobabilityThe probability of two events both occurring; that is, the probability ofthe intersection of two events.Generated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.:Judgmentsampling :A nonprobabilistic method of sampling whereby element selection isbased on the judgment of the person doing the study.Interquartilerange (IQR):A measure of variability, defined to be the difference between the thirdand first quartiles.Leastsquaresmethod :The method used to develop the estimated regression equation. Itminimizes the sum of squared residuals (the deviations between theobserved values of the dependent variable, yi, and the estimated values of

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the dependent variable, yi)Regressionequation :The equation that describes how the mean or expected value of thedependent variable is related to the independent variable.Rejectionregion :The range of values that will lead to the rejection of a null hypothesis.Replication:The number of times each experimental condition is repeated in anexperiment.Residual : The difference between the observed value of the dependent variable andthe value predicted using the estimated regression equation.Samplepoint :An element of the sample space. A sample point represents anexperimental outcome.Samplestatistic :A numerical value used as a summary measure for a sample (e.g., thesample mean, the sample variance, and the sample standard deviation).The value of the sample statistic is used to estimate the value of thepopulation parameter.Sampledpopulation:The population from which the sample is taken.Samplingunit :The units selected for sampling. A sampling unit may include severalelements.Samplingwithreplacement:Once an element has been included in the sample, it is returned to thepopulation. A previously selected element can be selected again andtherefore may appear in the sample more than once.Generated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Samplingwithoutreplacement:Once an element has been included in the sample, it is removed from thepopulation and cannot be selected a second time.Scatter

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diagram :A graph of bivariate data in which the independent variable is on thehorizontal axis and the dependent variable is on the vertical axis.Simplelinearregression :Regression analysis involving one independent variable and onedependent variable in which the relationship between the variables isapproximated by a straight line.Simplerandomsampling :Finite population: a sample selected such that each possible sample ofsize n has the same probability of being selected. Infinite population: asample selected such that each element comes from the same populationand the elements are selected independently.Standarderror :The standard deviation of a point estimator.Stem-andleafdisplay:An exploratory data analysis technique that simultaneously rank ordersquantitative data and provides insight about the shape of the distribution.Stratifiedrandomsampling :A probability sampling method in which the population is first dividedinto strata and a simple random sample is then taken from each stratum.Hypergeometricprobabilityfunction :The function used to compute the probability of x successes in ntrials when the trials are dependent.Multiplicationlaw :A probability law used to compute the probability of an intersection oftwo events, denoted A and B. It is P(AÇB)=P(A)P(B|A) or P(AÇB)=P(B)P(A|B). For independent events it reduces to P(AÇB)=P(A)P(B).Goodnessof fit test :A statistical test conducted to determine whether to reject a hypothesizedprobability distribution for a population.Samplingdistribution:A probability distribution consisting of all possible values of a samplestatistic.

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Question: What is the difference between cumulative frequency distribution andGenerated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Cumulative Frequency Polygon?.Answer: There is no difference between cumulative frequency distribution &Cumulative Frequency Polygon,because the graph of cummulativefrequency distrbution is known as Cumulative Frequency Polygon/ogive.Question: What is Frequency? What are the steps for making frequencydistribution?Answer: Frequency:It is a record of how often each value (or set of values) of the variable inquestion occurs. It may be enhanced by the addition of percentages that fall intoeach categorySteps in Frequency Distribution:Following are the basic rules to construct frequency distribution:1. Decide the number of classes into which the data are to be grouped& it depends upon the size of data.2. Determine the RANGE (difference between the smallest &largestvalues in data) data.3. Decide where to locate the class limit (numbers typically use toidentify the classes).4. Determine the reaming class limits by adding the class intervalrepeatedly.5. Distribute the data into classes by using tally marks and sum it infrequency column. Finally, total the frequency column to see that all data havebeen accounted for.Question: What is Box & Whisker Plot?Answer: Box and Whisker Plot (or Box plot):A box and whisker plot is a way of summarizing a set of data measuredon an interval scale. It is often used in exploratory data analysis. It is a type ofgraph which is used to show the shape of the distribution, its central value, andvariability. The picture produced consists of the most extreme values in the dataset (maximum and minimum values), the lower and upper quartiles, and themedian.A box plot (as it is often called) is especially helpful for indicating whether adistribution is skewed and whether there are any unusual observations (outliers)in the data set.Box and whisker plots are also very useful when large numbers of observationsare involved and when two or more data sets are being compared.Question: What is Mean, Median & Mode?Answer: Mean:The arithmetic mean is the statistician’s term for what the layman knows as theaverage. The arithmetic mean or simply the mean is a value obtained bydividing the sum of all the observations by their number.THE MEDIAN:The median is the middle value of the series when the variable values areplaced in order of magnitude.THE MODE:

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The mode is defined as that value which occurs most frequently in a setof data i.e. it indicates the most common result.The median indicates the middle position while the mode providesinformation about the most frequent value in the distribution or the set of data.Both median & mode are different methods of calculating the average value ofdata and they have their advantages & disadvantages .They are used by thestatisticians according to their requirement.Generated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Question: What is meant by Dispersion?Answer: Dispersion means the extent to which the data/values are spread out fromthe average.Example:There are many situations in which two different data having thesame average e.g.Data 1:5, 5,5,5,5 having mean=5Data 2:1, 5,6,6,7 having mean=5Hence in such a situation we, need a measure which tell us howdispersed the data are. The measure used for this purpose is calledmeasure of dispersion.Question: What is the relation between these two Moments & Moment Ratios . ?Answer: Moments: A moment designates the power to which deviations are raisedbefore averaging them. Moment ratio: These are certain ratios in whichboth numerators and the denominators are moments.Question: What is the difference between frequency and frequency distribution.?Answer: Frequency:The number of observations falling in a particular class isknown as class frequency or simply frequency.Frequency distribution.When we arrange the frequencies in a form of table then it isknown as Frequency distribution.Question: What is meant by standard deviation?.Answer: Standard deviation tells how tightly a set of values is clustered around theaverage of those same values.Question: What is the difference between these two limits when we are dealing withcontinuous random variable: 0<5 and 0 ≤ x ≤5 .Answer: In case ofcontinuous random variable there is no differecce both arediscribing the same thing either we mention the equal sign or not that is,the random variable ranging from 0 to 5.Question: What is the difference between the Poisson distribution and the normaldistribution?Answer: Poisson distribution. The Poisson distribution is referred to as thedistribution of rare events. Examples of Poisson distributed variables arenumber of accidents per person, number of sweepstakes won per person,or the number of catastrophic defects found in a production process.While: Normal Distribution. The normal distribution (the "bell-shapedcurve" which is symmetrical about the mean) is a theoretical functioncommonly used in inferential statistics as an approximation to sampling

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Generated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.distributions. In general, the normal distribution provides a good modelfor a random variable, when: There is a strong tendency for the variableto take a central value; Positive and negative deviations from this centralvalue are equally likely; The frequency of deviations falls off rapidly asthe deviations become larger.Question: What is the difference between type-I error and type -II error ?.Answer: Type-I error:In a hypothesis test, a type I error occurs when the nullhypothesis is rejected when it is in fact true; that is, H0 iswrongly rejected. For example, suppose that an accused is,in fact, innocent (i-e Ho is true) but the finding of the judgeis guilty. The judge has rejected the true null hypothesisand is so doing ,has made a type-I error.Type-II error:In a hypothesis test, a type II error occurs when the nullhypothesis H0, is not rejected when it is in fact false. Forexample if the accused is, in fact, guilty (i-e Ho is false) andthe finding of the judge is innocent, the judge has acceptedthe false null hypothesis and by accepting the false nullhypothesis he has committed a type –II error.Question: What is the difference between permutation and combination.Answer: Permutations:When our purpose is to arrange the objects with respect to orderout of" n" then we use permutations.Combinations:When we select our objects out of "n" with out considering orderthen we apply combination.Question: what is meant by marginal probability function?.Answer: The individual probability function of the random variables,from the jointprobability function,is known as marginal probability function.Question: What is ORDINAL or RANKING SCALE.Answer: Where nominal scales don't allow comparisons in degree, this is possiblewith ordinal scales. Say you think it is better to live in Karachi than inLahore but you don't know by how much. Example: 1-People or objectswith a higher scale value have more of some attribute. 2-The intervalsbetween adjacent scale values are indeterminate. 3-Scale assignment is bythe property of "greater than," "equal to," or "less than."Generated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Question: What is the descriptive and inferential Statistics.Answer: Descriptive Statistics uses graphical and numerical techniques tosummarize and display the information contained in a data set. InferentialStatistics uses sample data to make decisions or predictions about a largerpopulation of data.Question: What is Skewness?

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Answer: Skewness is defined as asymmetry in the distribution of the sample data values.Values on one side of the distribution tend to be further from the 'middle' thanvalues on the other side.For skewed data, the usual measures of location will give different values, forexample, mode<median<mean would indicate positive (or right) skewness.Positive (or right) skewness is more common than negative (or left) skewness.If there is evidence of skewness in the data, we can apply transformations, forexample, taking logarithms of positive skew data.Question: Define Variable,Discrete Variable and continuous Variable.Answer: Variable is a characteristic under study that assumes different values fordifferent elements. For example, Height of students in a class, No. ofrooms in a house Discrete Variable: A DISCRETE variable is one whichmay take on only a countable number of distinct values such as 0, 1, 2, 3,4,......... Discrete variables are usually (but not necessarily) counts. If avariable can take only a finite number of distinct values, then it must bediscrete. Examples of discrete variables include the number of children ina family, the Friday night attendance at a cinema, the number of patientsin a doctor's surgery, the number of defective light bulbs in a box of ten.Continuous Variable: A CONTINUOUS variable is one which takes aninfinite number of possible values. Continuous variables are usuallymeasurements. Examples include height, weight, the amount of sugar inan orange, the time required to run a mile.Question: What is correletion coefficient?Answer: Correlation Coefficient: A correlation coefficient is a number between -1and 1 which measures the degree to which two variables are linearlyrelated. If there is perfect linear relationship with positive slope betweenthe two variables, we have a correlation coefficient of 1; if there ispositive correlation, whenever one variable has a high (low) value, sodoes the other. If there is a perfect linear relationship with negative slopebetween the two variables, we have a correlation coefficient of -1; if thereis negative correlation, whenever one variable has a high (low) value; theother has a low (high) value. A correlation coefficient of 0 means thatthere is no linear relationship between the variables.Question: what is ment by percentile coefficient of kurtosis?Answer: Kurtosis: Karl Pearson introduced the term Kurtosis for the degree ofpeakedness or flatness of a unimodal frequency curve. Percentile Coefficientof Kurtosis is another measure of kurtosis which is not widelyused. it is given by K=Q.D/ P90 –P10 Where Q.D is the semi interGenerated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.quartile range & P’s are the percentiles. It has been shown that K for anormal distribution is .263 and it lies between 0 and 0.50.Question: Explain Conditional Probability, Marginal Probability and JointProbability.Answer: Conditional probability is the probability of some event A, assumingevent B. Conditional probability is written P(A|B), and is read "theprobability of A, given B". Joint probability is the probability of two

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events in conjunction. That is, it is the probability of both events together.The joint probability of A and B is written as P(AÇB) or P(A,B) orP(AB). Marginal probability is the probability of one event, ignoring anyinformation about the other event. Marginal probability is obtained bysumming (or integrating, more generally) the joint probability over theignored event. The marginal probability of A is written P(A), and themarginal probability of B is written P(B).Question: what is Random Variable?Answer: Random Variable: A random variable is a rule that assigns a value to eachpossible outcome of an experiment. For example, if an experimentinvolves measuring the height of people, then each person who could be asubject of the experiment has associated value, his or her height. Arandom variable may be discrete (the possible outcomes are finite, as intossing a coin) or continuous (the values can take any possible valuealong a range, as in height measurements).Question: Explain the Concept of "Continous Random Variable"Answer: Continuous random variable: A continuous random variable is one whichtakes an infinite number of possible values. Continuous random variablesare usually measurements. Examples include height, weight, the amountof sugar in an orange, the time required to run a mile.Question: Explain the concept of inferential statisticts.Answer: Inferential statistics: In Inferential Statistics we try to get an idea aboutpopulation parameters using sample data because it is not possible, inmany situations, for us to study the whole of population. We thereforeresort ourselves to the sample estimates. In drawing conclusion, thedecision maker makes use of probability theoryQuestion: What is continuity correction?Answer: Continuity Correction Factor A value of .5 that is added to and/orsubtracted from a value of a Binomial random variable X when thecontinuous normal probability distribution is used to approximate thediscrete binomial probability distributionQuestion: what is hypereomatric distribution.Answer: Hypergeometric Distribution: In probability theory and statistics, thehypergeometric distribution is a discrete probability distribution thatGenerated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.describes the number of successes in a sequence of n draws from a finitepopulation without replacement.Question: What is probablity density function and what is it's significance.Answer: Dear Student, Probability density function (pdf) is a mathematicalexpression or formula which gives probabilities for a range of values of acontinuous random variable. It is denoted by f(x). It has certain veryimportant properties which we have sent you by email. Probabilitydensity functions are of great significance in Statistics. In fact all theconclusions that are made in Inferencial Statistics are due to usingappropriate probability density function. Most important probabilitydistributions which are used in Inferencial Statistics are normaldistribution, t-distribution, F distribution and chi-square distribution.

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Question: What is random variable and how the fdp is related to it?Answer: RANDOM VARIABLE: Such a numerical quantity whose value isdetermined by the outcome of a random experiment is called a randomvariable. For example, no. of children in a family, daily income of amedical store etc. It is of two types (i) Discrete random variable (ii)Continuous random variable Probability density function (pdf) is theexpression or formula which gives us the probability for given range ofvalues of the continuous random variable.Question: What is the concept of normal distribution.Answer: Gaussian (Normal) Distribution The Normal or Gaussian distributionplays a central role in statistics and has been found to be a very goodmodel for many continuous distributions that occur in real situations. Thefunction is symmetric about the mean, it gains its maximum value at themean, the minimum value is at plus and minus infinity. The distributionis often referred to as "bell shaped".Question: Define Hypothetical population and non random sampling.Answer: Hypothetical population: A population is not necessarily real; it may behypothetical or imaginary. For example, outcomes of an experiment, thatis carried out infinitely, make a hypothetical population. It consists of allconceivable ways in which an event can occur, e.g. all possible throws ofa die. Such a population does not exist in an actual manner but is only tobe thought of. Non-random Sampling: ‘Nonrandom sampling’ impliesthat kind of sampling in which the population units are drawn into thesample by using one’s personal judgment. In this sampling personaljudgment (of an every person) decide that which sampling unit (ofpopulation) should be selected for the sample.Question: what are the main and detailable concept of dispersionAnswer: Dispersion means the extent to which the data/values are spread out fromthe average. Example: There are many situations in which two differentdata having the same average e.g. Data 1:5, 5,5,5,5 having mean=5 DataGenerated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.2:1, 5,6,6,7 having mean=5 Hence in such a situation we, need a measurewhich tell us how dispersed the data are. The measure used for thispurpose is called measure of dispersion.Question: if X1=20.7% and X2=14.56% then which is more variant? Explainrelative measure of dispersion?Answer: Suppose we have two distributions having coefficient of variations:CV(X1) =20.7% CV(X2) =14.56% Than the first distribution has morevariation as compare to second as: CV(X1)> CV(X2) Relative measure ofdispersion is one that is expressed in the form of a ratio, co-efficient ofpercentage and is independent of the units of measurement. A relativemeasure of dispersion is useful for comparison of data of different nature.A measure of central tendency together with a measure of dispersiongives an adequate description of data. We will be discussing FOURmeasures of dispersion i.e. the range, the quartile deviation, the meandeviation, and the standard deviation.Question: what is difference beween correlation and regression.

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Answer: Correlation: Correlation is a measure of the strength or the degree ofrelationship between two random variables. Or Interdependence of twovariables is called correlation. Regression: Dependence of one variableon the other variable is called regression. Or Estimation or prediction ofone variable on the basis of other variable is called regression.Question: What is population?Answer: A population is consist of the totality of the observation with which we reconcerned.Question: What is a Sample?Answer: A sample is a group of units selected from a larger group (the population). Bystudying the sample it is hoped to draw valid conclusions about the larger group.A sample is generally selected for study because the population is too large tostudy in its entirety. The sample should be representative of the generalpopulation. This is often best achieved by random sampling. Also, beforecollecting the sample, it is important that the researcher carefully and completelydefines the population, including a description of the members to be included.Example:The population for a study of infant health might be all children born in thePakistan in the 1980's. The sample might be all babies born on 7th May in anyof the years.Question: What is Statistic?Answer: A statistic is a quantity that is calculated from a sample of data.Question: In which distributions we used empirical rule & chebychev rule?.Answer: Empirical rule is applicable to the mound- shape, symmetrical andunimodle (bell shaped)distributions while chebychev apply to anyGenerated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.distribution regardless of the shape of the frequency distribution of thedata.Question: What are the different ways of representing the frequency distributiongraphically?Answer: There are three ways of graphical representation of frequency distribution.HISTOGRAM:A histogram consists of a set of adjacent rectangles whose basesare marked off by class boundaries along the X-axis, and whose heights areproportional to the frequencies associated with the respective classes.FREQUENCY POLYGON:A frequency polygon is obtained by plotting the class frequenciesagainst the mid-points of the classes, and connecting the points so obtained bystraight line segments.FREQUENCY CURVE:When the frequency polygon constructed over class intervalsmade sufficiently small for a large number observation, is smoothed, itapproaches a continuous curve, such a curve is called Frequency Curve.Types of Frequency Curves:The frequency distribution occurring in practice, usually belong to one of thefollowing four types. You will study about them in your next lecture.

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1. The Symmetrical Distribution.2. Moderately Skewed Distribution.3. Extremely Skewed or J-shaped Distribution4. U-Shaped DistributionQuestion: What is meant by 5-Number Summary?Answer: 5-Number Summary:A 5-number summary is especially useful when we have so many datathat it is sufficient to present a summary of the data rather than the whole dataset. It consists of 5 values: the most extreme values in the data set (maximumand minimum values), the lower and upper quartiles, and the median.A 5-number summary can be represented in a diagram known as a box andwhisker plot. In cases where we have more than one data set to analyze, a 5-number summary is constructed for each, with corresponding multiple box andwhisker plots.Question: What is meant by mid-rang and mid-quartile range and what is thedifference between these two ranges.?Answer: MID-RANGE: If there are n observations with x0 and xm as theirsmallest and largest observations respectively, then their mid-range isdefined as Mid range=X0+Xm/2. It is obvious that if we add the smallestvalue with the largest, and divide by 2, we will get a value which is moreor less in the middle of the data-set. MID-QUARTILE RANGE: If x1,x2… xn are n observations with Q1andQ3 as their first and third quartilesrespectively, then their mid-quartile range is defined as Mid Quartilerange= Q1+Q3 /2. Difference: They both used as measures of centraltendency because they both provide us with more or less the middle valueof data. The difference is that the mid-quartile range is an attempt toaddress the problem of the range being heavily dependent on extremescores. An mid-quartile range represents the middle 50% of the scores inthe distribution.Generated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Question: What is meant by Loaded die?.Answer: A biased die is known as Loaded die.Question: What is the difference between Probability distribution and samplingdistribution?.Answer: The probability distribution of any statistic (such as the mean, thestandard deviation, the proportion of successes in a sample, etc.) isknown as its sampling distribution.Question: DISCUSS STATUS,STATISTICS AND STATISTIC.Answer: Latin words status, meaning a political state is believed to be the origin ofthe word “statistics” Statistics: Today the word statistics is used in threedifferent meanings. Firstly, it is used in the sense of data for exampleprice statistics, death statistics etc Secondly, it is used as the plural of theword “statistic” meaning the information obtained from the sample data.Thirdly, it means the science of collecting, presenting, analyzing, andinterpreting the numerical facts obtained as a result of a survey.Question: Define the error of instrument in respect of the ratio measurment?Answer: Error of Instrument arises when we are measuring any quantity because

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of the fault in the measuring instrument. For ratio scale we can use thefollowing example. If a student’s weight is recorded as 60 kg (correct tothe nearest kilogram), his true weight in fact lies between 59.5 kg and60.5 kg, whereas a weight recorded as 60.00 kg means the true weight isknown to lie between 59.995 and 60.005 kg. Thus there is a difference,however small it may be between the measured value and the true value.This sort of departure from the true value is technically known as theerror of measurement.Question: what is difference between raw data and grouped data,please explain itwith some example.Answer: Raw data Data that have not been processed in any manner is called rawdata. It often refers to uncompressed text that is not stored in any priorityformat. It may also refer to recently captured data that may have beenplaced into a database structure, but not yet processed. Grouped data Thedata presented in the form of frequency distribution is also known asgrouped data.Question: Explain the Term hypothesis.Answer: Dear Student, The term Hypothesis is also called Statistical Hypothesisand it is defined as: “An assumption or statement about the value ofunknown population parameter which may or may not be true is calledStatistical hypothesis.” It is of two types: 1. Null Hypothesis 2.Alternative Hypothesis Null Hypothesis: Any hypothesis which is to betested for possible rejection under the assumption that it is true is calledNull Hypothesis. It is generally denoted by Ho. The hypothesis is usuallyGenerated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.assigned a numerical value. For example, suppose we think that theaverage height of students in all colleges is 62 inches. This statement istaken as null hypothesis and is written symbolically as Ho: μ = 62.Alternative Hypothesis: “Any other hypothesis which we accept when thenull hypothesis is rejected is called Alternative hypothesis” It is generallydenoted by H1 or HA. A null hypothesis is thus tested against analternative hypothesis H1. For example, if our null hypothesis is Ho: μ =62, then our alternative hypothesis my be H1: μ ≠ 62 or H1: μ > 62 orH1: μ < 62.Question: Explain relative measure of dispersionAnswer: Relative measure of dispersion is one that is expressed in the form of aratio, co-efficient of percentage and is independent of the units ofmeasurement. A relative measure of dispersion is useful for comparisonof data of different nature. A measure of central tendency together with ameasure of dispersion gives an adequate description of data. We will bediscussing four measures of dispersion i.e. the range, the quartiledeviation, the mean deviation, and the standard deviation.Question: WHAT IS MOMENTSAnswer: Moments are the arithmetic means of the powers to which the deviationsare raised. Thus the mean of the first power of the deviations from meanis the first moment about the mean; the mean of the second power of thedeviations from mean is the second moment about the mean and so on.

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First four moments about mean are defined as: m1 = (X – Xbar)/n m2 =(X – Xbar)2/n m3 = (X – Xbar)3/n m4 = (X – Xbar)4/nQuestion: What is difference between independent and independence variable.Answer: Two events A and B in the same sample space S, are defined to beindependent if the probability that one event occurs, is not affected bywhether the other event has or has not occurred. Two events A and B inthe same sample space S, are defined to be Dependent if the probabilitythat one event occurs, is affected by whether the other event has or hasnot occurred.Question: Explain the Condititional Probability with the help of example.Answer: In conditional probability we are dealing with two events .One event isthat for which we have to find the probability and about 2nd event wehave some priori information.To illustrate the concept of conditionalprobability let us consider an example. Let a die is rolled. S={1,2,3,4,5,6}A is the event of getting a" 5" & a prior information is given that on aparticular throw of a die ,the outcome is an odd number (event B) .HenceB={1,3,5}now the probability of getting a "5" in this reduce sample spaceis 1/3 which is known as conditional probability of event "A". Note.Priori means already known information before starting the experimentQuestion: what is loaded die?Generated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Answer: We can say that, a biased unfair die is a loaded dieQuestion: Explain Nominal and ordinal levels of measurement and also tell me whatis EPAmileage rating.Answer: Nominal Scales When measuring using a nominal scale, one simplynames or categorizes responses. The essential point about nominal scalesis that they do not imply any ordering. Nominal scales embody the lowestlevel of measurement. It is used for identifying individuals, groups orregions. Ordinal Scales Where nominal scales don't allow comparisons indegree, this is possible with ordinal scales. Say you think it is better tolive in Karachi than in Lahore but you don't know by how much. EPAmeans Environmental Protection Agency US government agency for theprotection of the environment which ranks the most fuel-efficient vehicle.Question: Explain bivarite.Answer: Bivariate Data Before we looked at one measurement on an observation(or individual), say X is height. Now we're interested in more than onemeasurement per observation (individual), say X is height and Y isweight. Let's say we have n individuals we're taking the measurementson. Then our data would be as follows (X1,Y1), (X2, Y2).....(Xn, Yn)Question: What is meadianAnswer: abcQuestion: Quartiles & their Uses.Answer: Quartile: The values which divide the distribution into four equal partsare called quartiles. Quartiles divide the data into four equal-sized andnon-overlapping parts. One fourth of the data lies below the Q1 (firstquartile). Half of the data lies below Q2 (second quartile) similarly, threequarters of the data lies below Q3 (third quartile) Q2 (second quartile) is

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also known as median. Use of quartiles: In order to describe a data setwithout listing all the data, we have measures of location such as themean and median, measures of spread such as the range and standarddeviation. Quartiles are also used to describe the data in combination withother measures. For example they are used in five number summary ofthe data. The five number summary, i.e., the minimum, Q1, Q2 (median),Q3, and maximum, give a good indication of where data lie. The fivenumber summary is sometimes represented graphically as a (box-and-)whisker plot.Question: ACCEPTANCE AND REJECTION REGIONS.Answer: ACCEPTANCE AND REJECTION REGIONS: All possible valueswhich a test-statistic may assume can be divided into two mutuallyexclusive groups: One group consisting of values which appear to beconsistent with the null hypothesis (i.e. values which appear to supportthe null hypothesis), and the other having values which lead to therejection of the null hypothesis The first group is called the acceptanceGenerated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.region and the second set of values is known as the rejection region for atest. The rejection region is also called the critical region.Question: Explain the concept of Cumulative Frequency.Answer: Cumulative frequency is used to determine the number of observationsthat lie above (or below) a particular value in a data set. The cumulativefrequency is calculated using a frequency distribution table. Thecumulative frequency is determined by adding each frequency from afrequency distribution table to the sum of its predecessors. The last valuewill always be equal to the total for all observations.Question: Difference between Skewed and symmetrical distribution.Answer: A frequency distribution or curve is said to be skewed when it departsfrom symmetry. If the right tail is longer the distribution is positivelyskewed and if the left tail of the distribution is longer, the distribution issaid to be negatively skewed. A frequency distribution or curve is said tobe symmetrical if values equidistant from a central maximum have thesame frequencies.Question: Explain the use of word STATISTICS in singula & plural sense.Answer: Latin words status, meaning a political state is believed to be the origin ofthe word “statistics” Statistics: Today the word statistics is used in threedifferent meaning. Firstly, it is used in the sense of data for example pricestatistics, death statistics etc Secondly, it is used as the plural of the word“statistic” meaning the information obtained from the sample data.Thirdly, it means the science of collecting, presenting, analyzing, andinterpreting the numerical facts obtained as a result of a survey.Question: State about the types of statistics ?Answer: Statistics as a subject is divided into descriptive and inferential statistics.Descriptive Statistics uses graphical and numerical techniques tosummarize and display the information contained in a data set. InferentialStatistics uses sample data to make decisions or predictions about a largerpopulation of data.

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Question: What is bais and how it is differnt from random error?Answer: A systematic error which deprive our resluts from thererepresentativeness. Biase id different from random error in the sence thatrandom error balance out in the long run while biase is cumulative(addition of error) and does not become balance out in long the run.Question: what is Point Estimation.Answer: Point estimation of a population parameter provides, as an estimate, asingle value calculated from the sample that is likely to be close in valueto the unknown parameter. For example the value of the statistic (Xbar)computed from a sample of size n, is a point estimate of the populationparameter (u)Generated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Question: state what is Grouped and Row data?Answer: Grouped data The data presented in the form of frequency distribution isalso known as grouped data. Raw data Data that have not been processedin any manner. It often refers to uncompressed text that is not stored inany priority format. It may also refer to recently captured data that mayhave been placed into a database structure, but not yet processed.Question: define theMean Deviation.Answer: The mean deviation is used to characterize the dispersion among themeasures in a given population. To calculate the mean deviation of a setof scores it is first necessary to compute their average (mean or median)and then specify the distance between each score and that mean withoutregard to whether the score is above or below( negative and positive) themean. The mean deviation is defined as the mean of these absolutevalues.Question: What is meant by variability?Answer: Variability is the spread or dispersion in a set of data. Consider thefollowing sets of data. 9, 9, 9, 9, 9, 9, 9, 9, 9, 9 10, 6, 2, 8, 4, 14, 16, 1213, 10, 7, 6, 21, 3, 7, 5 All these three sets of data have same mean ( 9 )but they are different in variability. First set of values has no dispersionand there is greater variability is third data set as compared to second setof data as its values are more spread away as compared to the values ofsecond set of data.Question: What is EQUALLY LIKELY EVENTS?Answer: The two events are said to be equally likely if they have the same chanceof occurring. For example, in our coin-tossing experiment, the twoevents, heads and tails, are equally likely. Both have the same chances ofoccurring. There is 50% chance for occurring both events.Question: What is meant by Transformation?Answer: If we change one variable into another variable, this is calledtransformation. For example, If we have values of variable X, then wecan find the values of other variables using transformations like Y = X +3 or Z = 2X - 5Question: Explain Primary and Secondary data.Answer: Primary and Secondary data: When people think of market research, theytend to think of collecting data directly from customers, prospects, or

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other stake holders (this is called primary data collection). However,secondary data can also provide a rich source of information. Secondarydata are data that already exist in industry-specific reports, previousresearch on the topic of interest, or data from an organization’s own database. Qualitative sources of secondary data include magazine andnewspaper articles and annual reports of industry participants.Generated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Question: What is Average?Answer: A single value used to represent the distribution is called average. Mostcommonly used averages are Mean, Median and Mode.Question: What is Ogive and polygon.Answer: In statistics, an ogive is the curve of a cumulative distribution function.polygon and ogive are same.Question: What is simple random and stratified sampling.Answer: Simple random sampling: With simple random sampling, each item in apopulation has an equal chance of inclusion in the sample. Stratifiedsampling: In stratified sampling, the population is divided into groupscalled strata. A sample is then drawn from within these strata. Someexamples of strata commonly used by the ABS are States, Age and Sex.Other strata may be religion, academic ability or marital status.Question: Define cluster sampling.Answer: Cluster sampling divides the population into groups, or clusters. Anumber of clusters are selected randomly to represent the population, andthen all units within selected clusters are included in the sample.Question: why we construct chart in Statistics?Answer: Charts are used to illustrate quantitative relationships between thevariables.Question: define the Distribution function.Answer: Distribution Function: The distribution function D(x) (also called thecumulative density function (CDF) or probability distribution function),describes the probability that a variate /variable X takes on a value lessthan or equal to a number x. The distribution function is sometimes alsodenoted by F(x) .The function F(x) gives the probability of the event thatX takes a value less than or equal to a specified value x.Question: How we calculate the boundries?Answer: CLASS BOUNDARIES The true class limits of a class are known as itsclass boundaries.It should be noted that the difference between the upperclass boundary and the lower class boundary of any class is equal to theclass interval.Question: what is value of central tendecy? and why weapply it ?and how manytypes of centeral tendencyAnswer: Central Tendency means the tendency of the data to gather around somecentral value and the value around which all the observations tend togather is called measure of central tendency. Measures of centraltendency of central tendency are generally known as Averages. The mostGenerated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.

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common types of averages are: i) The arithmetic mean ii) GeometricMean iii) Harmonic Mean iv) Median v) ModeQuestion: How we find mediam from the data?Answer: In order to find Median, we following the steps: i) Arrange the values inincreasing order. ii) Count the number of values. iii) a. If the no. of valuesis odd then Median is (n+1)/2 th value. b. If the no. of values is even thenMedian is the average of n/2 th and [(n/2) +1] th observations.Question: What is the relation between these two Moments & Moment Ratios?Answer: Moments: A moment designates the power to which deviations are raisedbefore averaging them. Moment ratio: These are certain ratios in whichboth numerators and the denominators are moments.Question: what is difference between arbitrary form and dispersion?Answer: Arbitrary form: We find the moment form any value other than the meanthat is called the moments about the arbitrary form. Dispersion: By whichwe mean the extent the observation in a sample or population are spreadout. And the second moment about the mean is exactly the same thing asthe variance, the positive square root of which is the standard deviation,the most important measure of dispersion?Question: what is the conditinal and un conditinal probability?Answer: In many situations, once more information becomes available, we areable to revise our estimates for the probability of further outcomes orevents happening. For example, suppose you go out for lunch at the sameplace and time every Friday and you are served lunch within 15 minuteswith probability 0.9. However, given that you notice that the restaurant isexceptionally busy, the probability of being served lunch within 15minutes may reduce to 0.7. This is the conditional probability of beingserved lunch within 15 minutes given that the restaurant is exceptionallybusyQuestion: explain What is Moment ratios?Answer: Moment ratios are certain ratios in which both the numerator and thedenominator are moments. The most common of these moment-ratios aredenoted by b1 and b2 and defined by the relations: i) b1 = (m3)2 / (m2)3ii) b2 = m4 / (m2)2 These are independent of origin and units ofmeasurement, i.e. they are pure numbers. b1 is used to measure theSkewness of distribution, and b2 is used to measure the kurtosis of thedistribution.Question: Why the significance level is consider 0.05?Answer: By a = 5%, we mean that there are about 5 chances in 100 of incorrectlyrejecting a true null hypothesis. That is, we want to make the significancelevel as small as possible in order to protect the null hypothesis and toprevent, as far as possible, the investigator from inadvertently makingGenerated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.false claims.Question: What is the difference between p(type 1 error) and p(type2 error)?Answer: Type I error: On the basis of sample information, we may reject the nullhypothesis H0, when it is, in fact true. This type of error is called the typeI error. Type II error: On the basis of sample information we may accept

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the null hypothesis H0, when it is actually false. This type of error iscalled the type II error.Question: write down the LAW OF COMPLEMENTATION and ADDITIONLAW.Answer: LAW OF COMPLEMENTATION: If A is the complement of an event Arelative to the sample space S, then P (A) = 1 – P (A) Complementaryprobabilities are very useful when we want to solve questions of the type‘What is the probability that, in tossing two fair dice, at least one evennumber will appear?’ ADDITION LAW If A and B are any two eventsdefined in a sample space S, then P (AÈB) = P (A) + P (B) – P (AÇB)Question: Define Multiplication theorem of probability for independent events.what is marginal probability.Answer: Multiplication theorem of probability for independent events is asfollows: P(A Ç B) = P(A) P(B) Here A and B are independents events.P(A) and P(B) are called marginal probabilities whereas, P(A Ç B) iscalled joint probability of A and B.Question: define sampling with replacement and sampling without replacement.Answer: In sampling with replacement, the units are replaced back before the nextunit is selected. In this sampling procedure, number of units in populationremains same for all selections. Let ‘N’ be the population size and ‘n’ bethe sample size then number of possible samples that can be drawn withreplacement are Nn. In sampling without replacement, the units are notreplaced back before the next unit is selected. In this sampling procedure,number of units in population is reduced after each unit. Let ‘N’ be thepopulation size and ‘n’ be the sample size then number of possiblesamples that can be drawn with replacement are NCn .Question: explain Point Estimator and what does it mean by a good point estimator.Answer: Point Estimator: A single value calculated from the sample that is likelyto be close in value to the unknown parameter. It is to be noted that apoint estimate will not, in general, be equal to the population parameteras the random sample used is one of the many possible samples whichcould be chosen from the population. Good Point Estimator: A pointestimator is considered a good estimator if it satisfies various criteria.Four of these criteria are: (i) Unbiasedness (ii) Consistency (iii)Efficiency (iv) SufficiencyQuestion: what is one Tailed and two TailedGenerated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.Answer: ONE-TAILED AND TWO-TAILED TESTS: A test, for which the entirerejection region lies in only one of the two tails – either in the right tail orin the left tail – of the sampling distribution of the test-statistic, is called aone-tailed test or one-sided test. If, on the other hand, the rejection regionis divided equally between the two tails of the sampling distribution ofthe test-statistic, the test is referred to as a two-tailed test or two-sidedtest.Question: What are the application of the and in which conditions for the use offollowing tests? F-test chi square test z-test and t-test are not fulfillingneed

32

Answer: (i) F-test is used to compare the variances of two populations. (ii) Chisquaretest is used to test a specific value of population variance. (iii) Ztestis used to test the mean of a population or equality of two populationmeans when population variance is known or sample size is greater than30. (iv) t-test is used to test the mean of a population or equality of twopopulation means when population variance is unknown or sample size isless than 30.Question: what is the difference between f-distribution , chi-square distribution tdistribution?Answer: These distributions have their own applications and these are used inseparate situations.(i) f-distribution is used to test the equality of two populationsvariances. It is also used to test the equality of populationmeans when we have more than two populations.(ii) t-distribution is used to test the mean of a population andequality of two population means in case of small sample size.(iii) Chi-square distribution is used to test the variance of apopulation. It is also used to test the association of attributes.Generated by Foxit PDF Creator © Foxit Softwarehttp://www.foxitsoftware.com For evaluation only.

18 - 32

Question # 1 of 10 ( Start time: 12:11:21 AM ) Total Marks: 1

Let X be a random variable with binomial distribution, that is (X=0,1,…, n). The expected value E[X] is

Select correct option:

p

np

np(1-p)

Xnp

Question # 2 of 10 Total Marks: 1

The sample mean is an unbiased estimator for the population mean. This means:


The sample mean has a normal distribution

33

The average sample mean, over all possible samples, equals the population mean

The sample mean is always very close to the population mean

The sample mean will only vary a little from the population mean


Probability of an impossible event is always:


Less than one

Greater than one

Between one and zero

Zero


The function abbreviated to d.f. is also called the......


Probability density function

Probability distribution function

Commutative distribution function

Discrete function


The total area under the normal curve is:


0

34

1

0.5

0.75


Two events A & B are said to be independent if....


P (A) + P (B)

P (B\A) = P (B)

P (A) * P (B)

P (A\B) = P (A)


When two coins are tossed the probability of at most one head is:


1/4

2/4

3/4

1


For exhaustive events, the P(AUBUC) is equal to:


P(A)

P(S)

P(A) * P(B)* P(C)

35

P(B)


One card is drawn from a standard 52 card deck. In describing the occurrence of two possible events, an Ace and a King, these two events are said to be:


independent

randomly independent

random variables

mutually exclusive


The number of parameters in hypergeometric distribution is (are):


1

2

3

4

State 30110 marks ka stem and leaf display thaprobability main s bohy kam ayaevent ki defor population ki def ai thi

IN another paper session

Long Q is

36

moments ka 10 marks kaand varience and SD ka 5 marks ka

1. 17 mcqs2.one long question of mode3.one question of chebychev's theoremjb kahein sy or information mely gi tu Inshallah zaroorshare karon gi.

My stats paper . . .Moment ratios - 10 marksprobability - 5 markscalculate the harmonic mean - 3 marksdefinition of sample - 1 markdefinition of population - 1 markand 16 mcq's

If X and Y are independent, then Var(X-Y) is equal to:

► ► ► ► Zero

Question No: 9 ( Marks: 1 )

Please choose one Which of the following is the class frequency

► The number of observations in each class

► The difference between consecutive lower class limits

► Always contains at least 5 observations

► Usually a multiple of the lower limit of the first class

Question No: 10 ( Marks: 1 ) - Please choose one How to construct the class interval:

► Divide the class frequencies in half

► Divide the class frequency by the number of observations

► Find the difference between consecutive lower class limits

► Count the number of observations in the class

Question No: 11 ( Marks: 1 ) - Please choose one Data in the Population Census Report is:

► Ungrouped data

► Secondary data

► Primary data

► Arrayed data

37

chck these 4 current papers of sta301

1st paper

10 marks ka stem and leaf display tha

probability main s bohy kam aya

event ki def

or population ki def ai thi

moments ka 10 marks ka

and varience and SD ka 5 marks ka

another

sta301 paper 2

sta301 me22 question hy,17 mcq the.

1marks ki defnation aye the

2marsks ka reason pocha tha

3marks ka mean wala sawal tha.

5marks ka moment ratio k formula or explaination aye thi..

10marks ki problem aye the solve ki the mene jo measure of dispersion se aye thi.

sta301 paper 3

Q1) find the low quartile and median. marks = 10

Q2) find the Range marks = 3

38

Q3) what is meant by Sample? marks= 2

Q4) it what situation we use the Emperical rule and bays therom? marks = 5

Q5) find the standared deviation? marks= 1

Q6) i think, objective type marks = 15

objective type ziada tar theory main say hi aya tha, koi question solve karnay k liay nhi dia gya tha,

e.g. mean > median > mode.

i) positively skewed

ii) negtively skewed

iii) equal

sta301 paper 4

friends main b isi bhol bolaye main tha ,par mera 80% paper probability main se aya,10 marks ka b 5 marks ka b,definatio 2 marks ki wo b prob se aur 11 mcqz from probability se

MIDTERM EXAMINATION

Spring 2009

STA301- Statistics and Probability (Session - 6)

Time: 60 min

Marks: 38

Question No: 1 ( Marks: 1 ) - Please choose one

39

For a positively skewed distribution m3 will be:

► Positive

► Negative

► Zero

► 1


When data is labeled to identify an attribute of element, the measurement scale is:

► Ordinal

► Interval

► Nominal

► Ratio


Suppose the estimated equation is has been calculated for a set of data. What is slop of the line:

► 0

► 2

40

► -2

► 5


If P(B|A) = 0.25 and , then P(A) is:

► 0.05

► 0.80

► 0.95

► 0.75


Which branch of statistics deals with the techniques that are used to organize, summarize, and present the data:

► Advance statistics

► Probability statistics

► Descriptive statistics

► Inferential statistics

41


In a sample of 800 students in a university, 160, or 20%, are Business majors. Based on the above information, the school's paper reported that "20% of all the students at the university are Business majors." This report is an example of :

► A sample

► A population

► Sstatistical inference

► Descriptive statistics


A set that contains all possible outcomes of a system is known as

► Finite Set

► Infinite Set

► Universal Set

► No of these


42

If X and Y are independent, then Var(X-Y) is equal to:

►

►

►

► Zero


Which of the following is the class frequency






How to construct the class interval:

► Divide the class frequencies in half

► Divide the class frequency by the number of observations

► Find the difference between consecutive lower class limits

43

► Count the number of observations in the class


Data in the Population Census Report is:

► Ungrouped data

► Secondary data

► Primary data

► Arrayed data


What is the range of -2,-3,-5,-10 :

► -12

► 8

► -8

44

► 2


The algebraic sum of deviations from mean is:

► Maximum

► Minimum

► Zero

► Undefined


The sum of squares of deviations from mean is:

► Undefined

► Zero

► Maximum

► Minimum


Statistic is a numerical quantity, which is calculated from:

45

► Population

► Sample

► Data

► Observations


Which of the following is not based on all the observations?

► Arithmetic Mean

► Geometric Mean

► Harmonic mean

► Mode


Elaborate the word dispersion.

We can say that the degree of scatter of data, usually about an average value, can be the median.


Define population.

46

We can define population is the collection of individuals or objects having some common measurable characteristics.


What does mean by the independence of two events:

We can define independence of two events are statistically independent if the probability of their occurring jointly equals the product of their respective probabilities. Independence of two events also know as stochastic independence.


The reciprocal of the values are

0.012, 0.0235, 0.0135

Calculate Harmonic Mean

Harmonic mean is 250.037


The probability that a student passes mathematics is 2/3 and the probability that he passes English is 4/9. If the probability of passing at least one course is 4/5, what is the probability that he will pass both courses?

47

Math=2/3

English=4/9

Least one passing probability= 4/5

Math + English =2/3+4/9

=1.11

4/5+1.11

=1.911


A pair of dice is thrown, then

1) Find the sample space for this experiment

Suppose if A and B is the pair of dice then lets try to find out how many result we can find

A hit first B Hit first B hit Second A Hit Second Both Hit Equally Both didn't Hit

48

2) Determine the probability of getting the sum 8 on the dice

3) Find the probability of getting sum 7 or 11

STA301 Online 5 Quizzesfrom Lectures 1-271. Question # 1 of 10 ( Start time: 08:23:14 PM ) Total Marks: 1If Y=bX, then variance of Y isSelect correct option:b*2 var(x)var(x)b var(x)b square root var(x)2. Question # 2 of 10 ( Start time: 08:24:38 PM ) Total Marks: 1If f(x) is a continuous probability function, then P(X = 2) is:Select correct option:101/223. Question # 3 of 10 ( Start time: 08:25:52 PM ) Total Marks: 1In regression line Y=a+bX, Y is called:Select correct option:Dependent variableIndependent variableExplanatory variableRegressor4. Question # 4 of 10 ( Start time: 08:26:51 PM ) Total Marks: 1If A and B are mutually exclusive events with P (A) =0.25 and P (B) = 0.50,Then P (A or B) =………Select correct option:0.250.750.5015. Question # 5 of 10 ( Start time: 08:28:06 PM ) Total Marks: 1Symbolically, a conditional probability is:Select correct option:P(AB)P(A/B)P(A)P(AUB)6. Question # 6 of 10 ( Start time: 08:28:42 PM ) Total Marks: 1In a 52 well shuffled pack of 52 playing cards, the probability of drawing any one

49

diamond card isSelect correct option:1/524/5213/5252/527. Question # 7 of 10 ( Start time: 08:30:13 PM ) Total Marks: 1Probability of a sure event isSelect correct option:8100.58. Question # 8 of 10 ( Start time: 08:31:42 PM ) Total Marks: 1If Y=3X+5,then S.D of Y is equal toSelect correct option:9 s.d(x)3 s.d(x)s.d(x)+53s.d(x)+5Question # 9 of 10 ( Start time: 08:33:16 PM ) Total Marks: 1The probability of drawing a red queen card from well-shuffled pack of 52 playingcards isSelect correct option:4/522/5213/5226/5210. Question # 10 of 10 ( Start time: 08:34:40 PM ) Total Marks: 1If P (B|A) = 0.25 and P (A and B) =0.20, then P (A) isSelect correct option:0.050.800.950.7511. Question # 1 of 10 ( Start time: 08:57:45 PM ) Total Marks: 1When a coin is tossed 3 times, the probability of getting 3 tails isSelect correct option:1/83/83/62/812. Question # 2 of 10 ( Start time: 08:59:14 PM ) Total Marks: 1In how many ways can a team of 11 players be chosen from a total of 16players?Select correct option:4368(not confirmed)2426

50

5400268013. Question # 3 of 10 ( Start time: 09:00:38 PM ) Total Marks: 1The standard deviation of c (constant) isSelect correct option:cc square0does not exist14. Question # 4 of 10 ( Start time: 09:01:46 PM ) Total Marks: 1If P (E) is the probability that an event will occur, which of the following must befalse:Select correct option:P(E)= - 1P(E)=1P(E)=1/2P(E)=1/3Question # 5 of 10 ( Start time: 09:02:48 PM ) Total Marks: 1Let E and F be events associated with the same experiment. Suppose the E andF are independent and that P(E) = 1/4 and P(F) = 1/2 Then P(E U F) is:Select correct option:1/83/47/85/816. Question # 6 of 10 ( Start time: 09:04:09 PM ) Total Marks: 1A student solved 25 questions from first 50 questions of a book to be solved. Theprobability that he will solve the remaining all questions is:Select correct option:0.250.51017. Question # 7 of 10 ( Start time: 09:05:31 PM ) Total Marks: 1If Y=bX, then variance of Y isSelect correct option:b*2 var(x)var(x)b var(x)b square root var(x)18. Question # 9 of 10 ( Start time: 09:07:48 PM ) Total Marks: 1The classical definition of probability assumes:Select correct option:Exhaustive eventsMutually exclusive eventsEqually likely evensIndependent evens19. Question # 10 of 10 ( Start time: 09:08:50 PM ) Total Marks: 1

51

In scatter diagram, the variable plotted along Y-axis is:Select correct option:Independent variableDependent variableContinuous variableDiscrete variable20. Which of the following measures of dispersion are based on deviationsfrom the mean?Select correct option:VarianceStandard deviationMean deviationAll of the these21. What does it mean when a data set has a standard deviation equal tozero?Select correct option:All values of the data appear with the same frequency.The mean of the data is also zero.All of the data have the same value.There are no data to begin with.22. A set of possible values that a random variable can assume and theirassociated probabilities of occurrence are referred to as ________.Select correct option:Probability distributionThe expected returnThe standard deviationCoefficient of variation23. Which of the following can never be probability of an event?Select correct option:010.5-0.524. The standard deviation of -1, -1, -1, -1 will beSelect correct option:1-10Does not exist25. Which formula represents the probability of the complement of eventA:Select correct option:1 + P (A)1 - P (A)P (A)P (A) -126. The Special Rule of Addition is used to combine:Select correct option:

52

Independent EventsMutually Exclusive EventsEvents that total more than 1.00Events based on subjective probabilities27. set which is the sub-set of every set isSelect correct option:Empty SetPower SetUniversal SetSuper Set28. E(4X + 5) =________Select correct option:12 E (X)4 E (X) + 516 E (X) + 516 E (X)29. When two dice are rolled the number of possible sample points is :Select correct option:612243630. Question # 1 of 10 ( Start time: 09:43:04 PM ) Total Marks: 1If two events A and B are not mutually exclusive thenSelect correct option:P (A or B) = P (A) + P (B) – P (A and B)P (A or B) = P (A) + P (B)P (A or B) = P (A) x P (B)P (A or B) = P (A) + P (B)31.Question # 2 of 10 ( Start time: 09:43:59 PM ) Total Marks: 1Evaluate (10-4)!Select correct option:10007204803232. Question # 3 of 10 ( Start time: 09:45:01 PM ) Total Marks: 1When E is an impossible event, then P(E) is:Select correct option:0120.533. Question # 4 of 10 ( Start time: 09:46:20 PM ) Total Marks: 1When we toss a coin , we get only:Select correct option:1 outcome

53

2 outcome3 outcome4 outcome34.Question # 5 of 10 ( Start time: 09:47:15 PM ) Total Marks: 1For exhaustive events, the P(AUBUC) is equal to:Select correct option:P(A)P(S)P(A) * P(B)* P(C)P(B)35. Question # 6 of 10 ( Start time: 09:48:21 PM ) Total Marks: 1A student solved 25 questions from first 50 questions of a book to be solved. Theprobability that he will solve the remaining all questions is:Select correct option:0.250.51036. A set of possible values that a random variable can assume and theirassociated probabilities of occurrence are referred to as ________.Select correct option:Probability distributionThe expected returnThe standard deviationCoefficient of variation37.Question # 9 of 10 ( Start time: 09:50:35 PM ) Total Marks: 1If we roll a die then probability of getting a ‘6’ will beSelect correct option:2/61/64/6138. Question # 10 of 10 ( Start time: 09:51:36 PM ) Total Marks: 1If P(A) = 0.45, P(B) = 0.35, and P(A and B) = 0.25, then P(A | B) is:Select correct option:1.41.80.7140.55639. Question # 8 of 10 ( Start time: 09:49:53 PM ) Total Marks: 1Which of the following is not a measure of central tendency?Select correct option:PercentileQuartileStandard deviationMode

54

40. Question # 1 of 10 ( Start time: 09:56:49 PM ) Total Marks: 1Random experiment can be repeated any no. of times under the……… conditions.Select correct option:DifferentSimilar42. Question # 3 of 10 ( Start time: 09:58:41 PM ) Total Marks: 1The simultaneous occurrence of two events is called:Select correct option:Joint probabilitySubjective probabilityPrior probabilityConditional probability43. Question # 4 of 10 ( Start time: 09:59:47 PM ) Total Marks: 1In regression analysis, the variable that is being predicted is theSelect correct option:Dependent variableIndependent variableIntervening variableNone of these


When each outcome of a sample space has equal chance to occur as any other, the outcomes are called:

► Mutually exclusive

► Equally likely

► Not mutually exclusive

► Exhaustive


55

The mean of the F-distribution is:

►

►

►

►


The LSD test is applied only if the null hypothesis is:

► Rejected

► Accepted

► No conclusion

► Acknowledged


56

Analysis of variance is a procedure that enables us to test the equality of several:

► Variances

► Means

► Proportions

► Groups


ANOVA was introduced by :

► Helmert

► Pearson

► R.A Fisher

► Francis


For testing of hypothesis about population proportion , we use:

► Z-test PROPORTIONS ARE TESTED AND MEAN

► t-Test MEAN IS TESTED

► Both Z & T-test

► F test VARIANCE AND STANDARD DEVIATION


57

If a random variable X denotes the number of heads when three distinct coins are tossed, the X assumed the values:

► 0,1,2,3

► 1,3,3,1

► 1, 2, 3

► 3, 2


If X and Y are independent variables, then E (XY) is:

► E(XX)

► E(X).E(Y)

► X.E(Y)

► Y.E(X)


The parameters of the binomial distribution b(x; n, p) are:

► x & n

► x & p

► n & p

► x, n & p

58


If P (E) is the probability that an event will occur, which of the following must be false:

► P(E)= - 1 ROBIBILITY SHOULD NEVER BE NEGATIVE AND NOT BE GREATER THAN ONE

► P(E)=1

► P(E)=1/2

► P(E)=1/3


An estimator T is said to be unbiased estimator of if

► E (T) =

EXPECTION OF STATISTIC IS EQUAL TO PARAMETER THAT IS ESTIMATED THEN STATISTIC IS CALLED UNBIASED OTHER WISE BIASED.

► E (T) =T

► E (T) =0

► E (T) =1


59

The best unbiased estimator for population variance is:

► Sample mean

► Sample median

► Sample proportion

► Sample variance


The sample variance is:

► Unbiased estimator of

► Biased estimator of

IF IT IS DI VIDED BY N-1 THEN IT IS CALLED UNBIASED OTHER WISE BIASED


► None of these

60


When c is a constant, then E(c) is:

1

0

c

-c

► 0

► 1

► c THE EXPECTION OF A CONSTATNT IS ALWAYS CONSTANT

► -c


If f (x, y) is bivariate probability density function of continuous r.v.'s X and Y then

is:

61

►

►

►

►


The analysis of variance technique is a method for :

► Comparing F distributions

► Comparing three or more means

► Measuring sampling error

► Comparing variances


The continuity correction factor is used when:

► The sample size is at least 5

► Both nP and n (1-P) are at least 30

► A continuous distribution is used to approximate a discrete distribution

62

► The standard normal distribution is applied


Stem and leaf is more informative when data is :

► Equal to 100

► Greater Than 100

► Less than 100

► In all situations


The branch of Statistics that is concerned with the procedures and methodology for obtaining valid conclusions is called:

► Descriptive Statistics

► Advance Statistics

► Inferential Statistics

► Sampled Statistics


Which of the following is a systematic arrangement of data into rows and columns?

63

► Classification

► Tabulation

► Bar chart

► Component bar chart


In normal distribution Q.D =

►

►

►

►


In normal distribution

► 1

► 2

► 3

64

► 0


If you connect the mid-points of rectangles in a histogram by a series of lines that also touches the x-axis from both ends, what will you get?

► Ogive

► Frequency polygon

► Frequency curve

► Historigram


Which one of the following statements is true regarding a population?

► It must be a large number of values

► It must refer to people

► It is a collection of individuals, objects, or measurements

► It is small part of whole


When ,what is the value of Median, if the distribution is

symmetrical:

► 1

► 2

► 3

65

► 4


In a simple linear regression model, if it is assumed that the intercept parameter is equal to zero, then:

► The regression line will pass through the origin

► The regression line will pass through the point (0,10).

► The regression line will pass through the point (0,-10).

► The slope of the line will also be equal to 0.


The degrees of freedom for a t-test with sample size 10 is:

► 5

► 8

► 9 n-1

► 10


In testing of hypothesis, we always begin it with assuming that:

► Null hypothesis is true

It is shown by h0 and first we assumption is h0

► Alternative hypothesis is true

66

► Sample size is large

► Population is normal


A failing student is passed by an examiner is an example of:

► Type I error

► Type II error

► Correct decision

► No information regarding student exams


How to find ?

► f(0, 0) + f(0, 1) + f(1, 2)

► f(2, 0) + f(0, 1) + f(1, 0)

► f(0, 0) + f(1, 1) + f(1, 0)

► f(0, 0) + f(0, 1) + f(1, 0)


How many parameters are involved in hypergeometric distribution?

67

Three N n k

Poission mean is np and variance and mean are equal


For a particular data the value of Pearson’s coefficient of skewness is greater then zero. What will be the shape of distribution?

► Negatively skewed

► J-shaped

► Symmetrical

► Positively skewed


In measures of relative dispersion unit of measurement is:

► Changed

► Vanish

► Does not changed

68

► Dependent


The F-distribution always ranges from:

► 0 to 1

► 0 to -∞

► -∞ to +∞

► 0 to +∞


In chi-square test of independence the degrees of freedom are:

► n - p

► n - p-1

► n - p- 2

► n – 2


The Chi- Square distribution is continuous distribution ranging from:

► -∞ ≤ χ2≤ ∞

69

► -∞ ≤χ2 ≤1

► -∞ ≤χ2 ≤0

► 0 ≤ χ2≤ ∞ 348


If X and Y are random variables, then is equal to:

►

►

►

► answr


If ŷ is the predicted value for a given x-value and b is the y-intercept then the equation of a regression line for an independent variable x and a dependent variable y is:

► ŷ = mx + b, where m = slope

► x = ŷ + mb, where m = slope

► ŷ = x/m + b, where m = slope

► ŷ = x + mb, where m = slope


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The location of the critical region depends upon:

► Null hypothesis

► Alternative hypothesis

► Value of alpha

► Value of test-statistic


The variance of the t-distribution is give by the formula:

►

►

►

►


Which one is the correct formula for finding desired sample size?

►

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►

►

►


A discrete probability function f(x) is always:

► Non-negative

► Negative

► One

► Zero


E(4X + 5) =__________

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► 12 E (X)

► 4 E (X) + 5

► 16 E (X) + 5

► 16 E (X)


How P(X + Y < 1) can be find:

► f(0, 0) + f(0, 1) + f(1, 2)

► f(2, 0) + f(0, 1) + f(1, 0)

► f(0, 0) + f(1, 1) + f(1, 0)

► f(0, 0) + f(0, 1) + f(1, 0)


The __________:

► 73

►

►

►


The area under a normal curve between 0 and -1.75 is

► .0401

► .5500

► .4599

► .9599


In normal distribution M.D. =

►

►

►

►

74


In an ANOVA test there are 5 observations in each of three treatments. The degrees of freedom in the numerator and denominator respectively are.......

► 2, 4

► 3, 15

► 3, 12

► 2, 12



► Finite Set

► Infinite Set

► Universal Set

► No of these



► Equal to 100


75

► Less than 100



A population that can be defined as the aggregate of all the conceivable ways in which a specified event can happen is known as:

► Infinite population

► Finite population

► Concrete population

► Hypothetical population

Question No. 01:

The number of telephone calls that pass through a switchboard has a Poison distribution with mean equal to 2 per minute. The probability that no telephone calls pass through the switchboard in two consecutive minutes is:


1. 0.27072. 0.05173. 0.01834. 0.0366

Question No. 02:

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The range of the binomial distribution is:


1. 0, 1, 2, ... , 1002. 0, 1, 2, … , n3. 0, 1, 2, … , x4. 1, 2, … , n

Question No. 03:

Which of the following is NOT CORRECT about a standard normal distribution?


1. P(0 ≤ Z ≤ 1.50) = .43322. P(Z ≥2.0) = .02283. P (Z ≥-2.5) = .49384. P (Z ≤ -1.0) = .1587

Question No. 04:

The distribution function (df) is also known as cumulative distribution function (cdf).


1. Yes2. No

Question No. 05:

Which of the following pairs of events are mutually exclusive?

Select correct option:77

1. A:the numbers above100;B: the numbers less than-2002. A:the odd numbers; B:the number 53. A:the even numbers; B:the numbers greater than 104. A:the numbers less than 5; B:all the negative numbers

Question No. 06:

Two events A & B are said to be independent if...


1. P(A) + P(B)2. P(B/A) = P(B)3. P(A) * P(B)4. P(A/B) = P(A)

Questions No. 07:

The collection of all outcomes for an experiment is called:


1. A sample space2. Joint probability simple event3. The intersection of events4. Random experiment

Question No. 08:

Symbolically, a conditional probability is:


1. P(AB)2. P(A/B)

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3. P(A)4. P(AUB)

Questions No. 09:

Which of the following statements is INCORRECT about the sampling distribution of the sample mean?


1. The standard error of the sample mean will decrease as the sample size increases

2. The standard error of the sample mean is measure of the variability of the sample mean among repeated samples

3. The sample mean is unbiased for the true (unknown) population mean4. The sampling distribution shows how the sample was distributed around

the sample mean

Question No. 10:

If one event is unaffected by the outcome of another event the two events are said to be:


1. Dependent2. Not Mutually Exclusive3. Mutually Exclusive4. Independent


Let X be a random variable with binomial distribution, that is (X=0,1,…, n). The expected value E[X] is

79


p

np

np(1-p)

Xnp


The sample mean is an unbiased estimator for the population mean. This means:


The sample mean has a normal distribution

The average sample mean, over all possible samples, equals the population mean

The sample mean is always very close to the population mean

The sample mean will only vary a little from the population mean




Less than one

Greater than one


Zero


The function abbreviated to d.f. is also called the......


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Probability density function

Probability distribution function

Commutative distribution function

Discrete function


The total area under the normal curve is:


0

1

0.5

0.75


Two events A & B are said to be independent if....


P (A) + P (B)

P (B\A) = P (B)

P (A) * P (B)

P (A\B) = P (A)


When two coins are tossed the probability of at most one head is:


81

1/4

2/4

3/4

1


For exhaustive events, the P(AUBUC) is equal to:


P(A)

P(S)

P(A) * P(B)* P(C)

P(B)


One card is drawn from a standard 52 card deck. In describing the occurrence of two possible events, an Ace and a King, these two events are said to be:


independent

randomly independent

random variables

mutually exclusive


The number of parameters in hypergeometric distribution is (are):


82

1

2

3

4

FINALTERM EXAMINATIONSpring 2010STA301- Statistics and Probability (Session - 4)Student InfoStudentID:Center:ExamDate: 08 Aug 2010For Teacher's Use OnlyQNo.1 2 3 4 5 6 7 8 TotalMarksQ No. 9 10 11 12 13 14 15 16MarksQ No. 17 18 19 20 21 22 23 24MarksQ No. 25 26 27 28 29 30 31 32MarksQ No. 33 34 35 36 37 38 39MarksSolved By WajidQuestion No: 1 ( Marks: 1 ) - Please choose oneWhen each outcome of a sample space has equal chance to occur as any other, theoutcomes are called:► Mutually exclusive► Equally likely► Not mutually exclusive► ExhaustiveQuestion No: 2 ( Marks: 1 ) - Please choose oneThemean of the F-distribution is:►22 1

11 forv

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vv►22 22

2 forvvv►22 1

11 forvvv►22 1

22 forvvvQuestion No: 3 ( Marks: 1 ) - Please choose oneTheLSD test is applied only if the null hypothesis is:► Rejected► Accepted► No conclusion► AcknowledgedQuestion No: 4 ( Marks: 1 ) - Please choose oneSolved By WajidAnalysis of variance is a procedure that enables us to test the equality of several:► Variances► Means► Proportions► GroupsQuestion No: 5 ( Marks: 1 ) - Please choose oneANOVA was introduced by :► Helmert

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► Pearson► R.A Fisher► FrancisQuestion No: 6 ( Marks: 1 ) - Please choose oneFor testing of hypothesis about population proportion , we use:► Z-test PROPORTIONS ARE TESTED AND MEAN► t-Test MEAN IS TESTED► Both Z & T-test► F test VARIANCE AND STANDARD DEVIATIONQuestion No: 7 ( Marks: 1 ) - Please choose oneIf arandom variable X denotes the number of heads when three distinct coins are tossed,the X assumed the values:► 0,1,2,3► 1,3,3,1► 1, 2, 3► 3, 2Question No: 8 ( Marks: 1 ) - Please choose oneIf Xand Y are independent variables, then E (XY) is:► E(XX)► E(X).E(Y)► X.E(Y)► Y.E(X)Question No: 9 ( Marks: 1 ) - Please choose oneSolved By WajidTheparameters of the binomial distribution b(x; n, p) are:► x & n► x & p► n & p► x, n & pQuestion No: 10 ( Marks: 1 ) - Please choose oneIf P(E) is the probability that an event will occur, which of the following must be false:► P(E)= - 1 ROBIBILITY SHOULD NEVER BE NEGATIVE AND NOT BE GREATER THANONE► P(E)=1► P(E)=1/2► P(E)=1/3Question No: 11 ( Marks: 1 ) - Please choose oneAn estimator T is said to be unbiased estimator of if► E (T) =EXPECTION OF STATISTIC IS EQUAL TO PARAMETER THAT IS ESTIMATED THEN STATISTIC

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IS CALLED UNBIASED OTHER WISE BIASED.► E (T) =T► E (T) =0► E (T) =1Question No: 12 ( Marks: 1 ) - Please choose oneThe best unbiased estimator for population variance 2

is:► Sample mean► Sample median► Sample proportion► Sample varianceSolved By WajidQuestion No: 13 ( Marks: 1 ) - Please choose oneThe sample variance2S2 (x x)n is:► Unbiased estimator of 2

► Biased estimator of 2

IF IT IS DI VIDED BY N-1 THEN IT IS CALLED UNBIASED OTHER WISE BIASED► Unbiased estimator of► None of theseQuestion No: 14 ( Marks: 1 ) - Please choose oneWhen c is a constant, then E(c) is:10c-c► 0► 1► c THE EXPECTION OF A CONSTATNT IS ALWAYS CONSTANT► -cQuestion No: 15 ( Marks: 1 ) - Please choose oneIf f(x, y) is bivariate probability density function of continuous r.v.'s X and Y theng(x)is:Solved By Wajid►

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f x, y dx►

f x, y dy

►f x, ydx dy ► , b da c

f x y dy dxQuestion No: 16 ( Marks: 1 ) - Please choose oneTheanalysis of variance technique is a method for :► Comparing F distributions► Comparing three or more means► Measuring sampling error► Comparing variancesQuestion No: 17 ( Marks: 1 ) - Please choose oneThe continuity correction factor is used when:



► A continuous distribution is used to approximate a discrete distribution► The standard normal distribution is appliedQuestion No: 18 ( Marks: 1 ) - Please choose oneStem and leaf is more informative when data is :► Equal to 100► Greater Than 100► Less than 100Solved By Wajid► In all situationsQuestion No: 19 ( Marks: 1 ) - Please choose oneThebranch of Statistics that is concerned with the procedures and methodology for obtaining valid

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conclusions is called:► Descriptive Statistics► Advance Statistics► Inferential Statistics► Sampled StatisticsQuestion No: 20 ( Marks: 1 ) - Please choose oneWhich of the following is a systematic arrangement of data into rows and columns?► Classification► Tabulation► Bar chart► Component bar chartQuestion No: 21 ( Marks: 1 ) - Please choose oneInnormal distribution Q.D =► 0.5► 0.75► 0.7979

► 0.6745Question No: 22 ( Marks: 1 ) - Please choose oneInnormal distribution 2 ► 1► 2► 3► 0Solved By WajidQuestion No: 23 ( Marks: 1 ) - Please choose oneIfyou connect the mid-points of rectangles in a histogram by a series of lines that alsotouches the x-axis from both ends, what will you get?► Ogive► Frequency polygon► Frequency curve► HistorigramQuestion No: 24 ( Marks: 1 ) - Please choose oneWhich one of the following statements is true regarding a population?► It must be a large number of values► It must refer to people► It is a collection of individuals, objects, or measurements► It is small part of wholeQuestion No: 25 ( Marks: 1 ) - Please choose oneWhenQ1 2 and Q3 4,what is the value of Median, if the distribution is symmetrical:► 1► 2

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► 3► 4Question No: 26 ( Marks: 1 ) - Please choose oneIn asimple linear regression model, if it is assumed that the intercept parameter is equal tozero, then:► The regression line will pass through the origin► The regression line will pass through the point (0,10).► The regression line will pass through the point (0,-10).► The slope of the line will also be equal to 0.Question No: 27 ( Marks: 1 ) - Please choose oneThedegrees of freedom for a t-test with sample size 10 is:► 5► 8► 9 n-1► 10Question No: 28 ( Marks: 1 ) - Please choose oneSolved By WajidIntesting of hypothesis, we always begin it with assuming that:► Null hypothesis is trueIt is shown by h0 and first we assumption is h0► Alternative hypothesis is true► Sample size is large► Population is normalQuestion No: 29 ( Marks: 1 ) - Please choose oneAfailing student is passed by an examiner is an example of:► Type I error► Type II error► Correct decision► No information regarding student examsQuestion No: 30 ( Marks: 1 ) - Please choose oneHow to findP(X Y 1)?► f(0, 0) + f(0, 1) + f(1, 2)► f(2, 0) + f(0, 1) + f(1, 0)► f(0, 0) + f(1, 1) + f(1, 0)► f(0, 0) + f(0, 1) + f(1, 0)Question No: 31 ( Marks: 2 )How many parameters are involved in hypergeometric distribution?Three N n kPoission mean is np and variance and mean are equalQuestion No: 32 ( Marks: 2 )

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Ifan automobile is driven on the average no more than 16000 Km per year, thenformulate the null and alternative hypothesis.Solved By Wajid011600016000HHQuestion No: 33 ( Marks: 2 )Write down the test statistic when chi- square goodness of fit test is performed.Question No: 34 ( Marks: 3 )Find the value of F(table value), when n1 7 , 2 n 10 and α= 0.053.37Question No: 35 ( Marks: 3 )If X= 327, n = 634, 0 p 0.50 then find the z-test statistic for proportion.Question No: 36 ( Marks: 3 )Ifpopulation proportions are given as:Find1 22ˆ

p pˆ ,where n = 101 22ˆ

p pˆ = p1q1/n1+p2q2/n2Question No: 37 ( Marks: 5 )Acandidate for mayor in a large city hires the services of a poll-taking organization, andthey found that 62 of 100 educated voters interviewed support the candidate, and 69 of150 uneducated voters support him.At the 0.05 significance level, test the following1 2 : 0.05 o H P P 1 1 2 H : P P 0.051 2 P 0.30, P 0.20.Solved By WajidBook Example # 16.17 on Page 155Professor sher Muhammad Chaudhry

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Question No: 38 ( Marks: 5 )Ifwe have RCBD with MSE=3.19, no.of.treatments = 4, no.of.blocks = 5; then find thevalue of LSD (least significant difference) for treatments by using α=0.05 and errordegrees of freedom is 12.Question No: 39 ( Marks: 5 )Find the mean and variance for the sampling distribution given below.pˆ No. ofSamplesProbability

f pˆ 0 1 1/201/3 9 9/202/3 9 9/201 1 1/20

20 1 PF( P ) 2

P PF( P ) 2

P F( P )0 1/201/3 9/202/3 9/201 1/20 1

Mean= =P f P

Variance= E(x)2 P 2 f P (P f P )2

Stat301 final term papersSolved By WajidQuestion No: 1 ( Marks: 1 ) - Please choose oneFora particular data the value of Pearson’s coefficient of skewness is greater then zero. What will bethe shape of distribution?► Negatively skewed► J-shaped► Symmetrical► Positively skewedQuestion No: 2 ( Marks: 1 ) - Please choose oneIn measures of relative dispersion unit of measurement is:► Changed► Vanish► Does not changed► Dependent

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Question No: 3 ( Marks: 1 ) - Please choose oneTheF-distribution always ranges from:► 0 to 1► 0 to -∞► -∞ to +∞► 0 to +∞Question No: 4 ( Marks: 1 ) - Please choose oneInchi-square test of independence the degrees of freedom are:► n - p► n - p-1► n - p- 2► n – 2Question No: 5 ( Marks: 1 ) - Please choose oneTheChi- Square distribution is continuous distribution ranging from:Solved By Wajid► -∞ ≤ χ2≤ ∞► -∞ ≤χ2 ≤1► -∞ ≤χ2 ≤0► 0 ≤ χ2≤ ∞ 348Question No: 6 ( Marks: 1 ) - Please choose oneIf Xand Y are random variables, then

E X Y is equal to:►E X ) E(Y ►E X ) E(Y ►X E Y ►E X Y answrQuestion No: 7 ( Marks: 1 ) - Please choose oneIf ŷis the predicted value for a given x-value and b is the y-intercept then the equation of aregression line for an independent variable x and a dependent variable y is:► ŷ = mx + b, where m = slope► x = ŷ + mb, where m = slope► ŷ = x/m + b, where m = slope► ŷ = x + mb, where m = slopeQuestion No: 8 ( Marks: 1 ) - Please choose one

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Thelocation of the critical region depends upon:► Null hypothesis► Alternative hypothesis► Value of alpha► Value of test-statisticQuestion No: 9 ( Marks: 1 ) - Please choose oneThevariance of the t-distribution is give by the formula:►22Solved By Wajid►222►12►22Question No: 10 ( Marks: 1 ) - Please choose oneWhich one is the correct formula for finding desired sample size?►2

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2Z .ne ►22Z .ne ►22Z .Xne ►2Z .ne Question No: 11 ( Marks: 1 ) - Please choose oneAdiscrete probability function f(x) is always:► Non-negative► Negative► One► ZeroSolved By WajidQuestion No: 12 ( Marks: 1 ) - Please choose oneE(4X + 5) =__________► 12 E (X)► 4 E (X) + 5

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► 16 E (X) + 5► 16 E (X)Question No: 13 ( Marks: 1 ) - Please choose oneHow P(X + Y < 1) can be find:► f(0, 0) + f(0, 1) + f(1, 2)► f(2, 0) + f(0, 1) + f(1, 0)► f(0, 0) + f(1, 1) + f(1, 0)► f(0, 0) + f(0, 1) + f(1, 0)Question No: 14 ( Marks: 1 ) - Please choose oneThe

f x |1 __________:►f 1,1►f x,1► ,11f xhSolved By Wajid► f x,1h xQuestion No: 15 ( Marks: 1 ) - Please choose oneThearea under a normal curve between 0 and -1.75 is► .0401► .5500► .4599► .9599Question No: 16 ( Marks: 1 ) - Please choose oneInnormal distribution M.D. =► 0.5► 0.75► 0.7979► 0.6445Question No: 17 ( Marks: 1 ) - Please choose oneInan ANOVA test there are 5 observations in each of three treatments. The degrees of

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freedom in the numerator and denominator respectively are.......► 2, 4► 3, 15► 3, 12► 2, 12Question No: 18 ( Marks: 1 ) - Please choose oneA set that contains all possible outcomes of a system is known as► Finite Set► Infinite Set► Universal Set► No of theseQuestion No: 19 ( Marks: 1 ) - Please choose oneSolved By WajidStemand leaf is more informative when data is :► Equal to 100► Greater Than 100► Less than 100► In all situationsQuestion No: 20 ( Marks: 1 ) - Please choose oneApopulation that can be defined as the aggregate of all the conceivable ways in which a specified event canhappen is known as:► Infinite population► Finite population► Concrete population► Hypothetical populationQuestion No: 21 ( Marks: 1 )If E(T) , what do you say about the estimator T, where is a parameter ?Question No: 22 ( Marks: 2 )What is a binomial experiment?Question No: 23 ( Marks: 3 )Formulate the null and alternative hypothesis in each of the following.(1) Average domestic consumption of electricity is 50 units per month.(2) Not more than 30% people pay Zakat (tax).Question No: 24 ( Marks: 3 )What is mathematical expectation of discrete random variable?Question No: 25 ( Marks: 3 )Why we prefer to use pooled estimatorˆc pQuestion No: 26 ( Marks: 3 )Solved By WajidDifferentiate between grouped and ungrouped data.Question No: 27 ( Marks: 5 )A

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population 2, 4, 6, 8, 10, 12N=6, n=2After drawing possible samples, we have calculated sampling mean7 x u andsampling variance2 5.833 x . Verify2) , ) 2 x x a bn Question No: 28 ( Marks: 5 )Arandom sample of size n is drawn from normal population with mean 5 and variance 2 .Answer the following:If s=15, x =14 and t=3, what is values of n?Question No: 29 ( Marks: 5 )Given the Probability density function.Compute the distribution function F(x).Question No: 30 ( Marks: 10 )An urn contains nine balls; five of them are red and four blue. Three balls are drawnwithout replacement. Find the distribution of X= number of red balls drawn.Question No: 31 ( Marks: 10 )Aresearch worker wishes to estimate the mean of a population using a sample sufficientlylarge that the probability will be 0.95 that the sample mean will not differ from the true elsewherefor xf xx0,, 0 2 2

Solved By Wajidmean by more than 25 percent of the standard deviation. How large a sample should betaken?Paper 2Question No: 1 ( Marks: 1 ) - Please choose one

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10!=………….► 362880► 3628800► 362280► 362800Question No: 2 ( Marks: 1 ) - Please choose oneWhen E is an impossible event, then P(E) is:► 2► 0► 0.5► 1Question No: 3 ( Marks: 1 ) - Please choose oneThevalue of χ2can never be :► Zero► Less than 1► Greater than 1► NegativeQuestion No: 4 ( Marks: 1 ) - Please choose oneThecurve of the F- distribution depends upon:► Degrees of freedom► Sample size► Mean► VarianceQuestion No: 5 ( Marks: 1 ) - Please choose oneIf Xand Y are random variables, then

E X Y is equal to:Solved By Wajid►E X ) E(Y ►E X ) E(Y ►X E Y ►E X YQuestion No: 6 ( Marks: 1 ) - Please choose oneIntesting hypothesis, we always begin it with assuming that:► Null hypothesis is true► Alternative hypothesis is true

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► Sample size is large► Population is normalQuestion No: 7 ( Marks: 1 ) - Please choose oneForthe Poisson distribution P(x) =0.135 0.13511! the mean value is :► 2► 5► 10► 0.135Question No: 8 ( Marks: 1 ) - Please choose oneWhen two coins are tossed simultaneously, P (one head) is:►14►12►34► 1Question No: 9 ( Marks: 1 ) - Please choose oneSolved By WajidFrom point estimation, we always get:► Single value► Two values► Range of values► ZeroQuestion No: 10 ( Marks: 1 ) - Please choose oneThe sample variance2S2 (x x)n is:► Unbiased estimator of 2


► Unbiased estimator of► None of these

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Question No: 11 ( Marks: 1 ) - Please choose oneVar(4X + 5) =__________► 16 Var (X)► 16 Var (X) + 5► 4 Var (X) + 5► 12 Var (X)Question No: 12 ( Marks: 1 ) - Please choose oneWhen f (x, y) is bivariate probability density function of continuous r.v.'s X and Y, then

f x, ydx dy is equal to:Solved By Wajid► 1► 0► -1► Question No: 13 ( Marks: 1 ) - Please choose oneThearea under a normal curve between 0 and -1.75 is► .0401► .5500► .4599► .9599Question No: 14 ( Marks: 1 ) - Please choose oneWhen a fair die is rolled, the sample space consists of:► 2 outcomes► 6 outcomes► 36 outcomes► 16 outcomesQuestion No: 15 ( Marks: 1 ) - Please choose oneWhen testing for independence in a contingency table with 3 rows and 4 columns, there are________ degrees of freedom.► 5► 6► 7► 12Question No: 16 ( Marks: 1 ) - Please choose oneTheF- test statistic in one-way ANOVA is:► SSW / SSE► MSW / MSE► SSE / SSW

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► MSE / MSWQuestion No: 17 ( Marks: 1 ) - Please choose oneThe continuity correction factor is used when:► The sample size is at least 5► Both nP and n (1-P) are at least 30Solved By Wajid► A continuous distribution is used to approximate a discrete distribution► The standard normal distribution is appliedQuestion No: 18 ( Marks: 1 ) - Please choose oneA uniform distribution is defined by:► Its largest and smallest value► Smallest value► Largest value► Mid valueQuestion No: 19 ( Marks: 1 ) - Please choose oneWhich graph is made by plotting the mid point and frequencies?► Frequency polygon► Ogive► Histogram► Frequency curveQuestion No: 20 ( Marks: 1 ) - Please choose oneIn aset of 20 values all the values are 10, what is the value of median?► 2► 5► 10► 20Question No: 21 ( Marks: 1 )If

P X 0=18,

P X 1=38,

P X 2=38andP(X 3)=

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18Then find F (1)Question No: 22 ( Marks: 2 )Write down the formula of mathematical expectation.e=(w * p) + (-v *1). eQuestion No: 23 ( Marks: 3 )Solved By WajidDiscuss the statistical independence of two discrete random variables:Question No: 24 ( Marks: 3 )Forgiven data calculate the mean and standard deviation of sampling distribution of mean if thesampling is down without replacement.N 1000, n 25, 68.5, 2.7Question No: 25 ( Marks: 3 )Elaborate the Least Significant Difference (LSD) Test.Question No: 26 ( Marks: 3 )Statethe Bayes’ Theorem.Question No: 27 ( Marks: 5 )Themeans and variances of the weekly incomes in rupees of two samples of workers are given in thefollowing table, the samples being randomly drawn from two different factories:Calculate the 90% confidence interval for the real difference in the incomes of the workers fromthe two factories.Question No: 28 ( Marks: 5 )From the given datan 1340, x 723, p .54and 0 0 1 0 H : P 0.5against H : P 0.5.Carry out the significance test for the stated hypothesis.Question No: 29 ( Marks: 5 )Factory Sample Size Mean VarianceA 160 12.80 64B 220 11.25 47Solved By WajidGiven the Probability density function.Compute the distribution function F(x).Question No: 30 ( Marks: 10 )f(x,y) 1 (6 – x – y), 0 x 2; 2 y 4,80, elsewhere

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a) Verify that f(x,y) is a jointdensity function.b) Calculate,2,Y 52P X 3 Question No: 31 ( Marks: 10 )Let1 2 3 X , X , Xbe a random sample of size 3 from a population with mean and variance 2

Consider the following two estimators of the mean1 2 311 2 32324T X X XT X X X Which estimator should be preferred?Stat final informationTotal question 3121 was mcqs and 10 was subjective questions.2 was of 10,10 marks2 was of 5,5 marks4 was of 3,3 marks these question ware about properties and 1 was aboutconfidece interval elsewherefor xf xx0,

103

, 0 2 2

Solved By Wajid2 was of 1, 1 marks, these question were only about defitions.1) 1 question from confidence interval , question was of 3 marks,find the confidence interval for difference between two ( papolation means) u1 , u2,ye question handouts main say hi aya tha, i think lecture no 35 main say tha.2) 1 question from hypotheyes testing ( Z- test) , marks 103) 2 questions was about properties, one was, write the properties of binomial distribution. andother was ,what is the good point estimator?4) 1 question was from lecture no 23 , this was of 3 markspage no 172, 1st example was same to same.find the F(x) of { 1, 2}x and f( x) was given.Definition estimate n estimator: x is poisson random variable with U(meu) =2 find (x=0)(x=1)(x=2)Q : joint probabilty distribution ka ta...bht ezy table dia ta find px=0/y=1Q: hypergeometric distibution ka ta....Q: confidence interval level ka ta...or baki choty choty shy....like why we use t-value...,.s^2 ia approx equall to S^2 how....FINALTERM EXAMINATIONFall 2009STA301- Statistics and Probability (Session - 1)Ref No: 1319492Time: 120 minMarks: 70Student InfoStudentID:Center: OPKSTExamDate: 2/24/2010 12:00:00 AMFor Teacher's Use OnlyQ No. 1 2 3 4 5 6 7 8 TotalMarksQ No. 9 10 11 12 13 14 15 16Solved By WajidMarksQ No. 17 18 19 20 21 22 23 24MarksQ No. 25 26 27 28 29 30 31MarksSolved By WajidQuestion No: 1 ( Marks: 1 ) - Please choose one10!=………….► 362880► 3628800

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► 362280► 362800Question No: 2 ( Marks: 1 ) - Please choose oneWhen E is an impossible event, then P(E) is:► 2► 0► 0.5► 1Question No: 3 ( Marks: 1 ) - Please choose oneThevalue of χ2can never be :► Zero► Less than 1► Greater than 1► NegativeQuestion No: 4 ( Marks: 1 ) - Please choose oneThecurve of the F- distribution depends upon:► Degrees of freedom► Sample size► Mean► VarianceQuestion No: 5 ( Marks: 1 ) - Please choose oneIf Xand Y are random variables, then

E X Y is equal to:►E X ) E(Y ►E X ) E(Y Solved By Wajid►X E Y ►E X YQuestion No: 6 ( Marks: 1 ) - Please choose oneIntesting hypothesis, we always begin it with assuming that:► Null hypothesis is true► Alternative hypothesis is true► Sample size is large► Population is normalQuestion No: 7 ( Marks: 1 ) - Please choose oneFor

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the Poisson distribution P(x) =0.135 0.13511! the mean value is :► 2► 5► 10► 0.135Question No: 8 ( Marks: 1 ) - Please choose oneWhen two coins are tossed simultaneously, P (one head) is:►14►12►34► 1Question No: 9 ( Marks: 1 ) - Please choose oneFrom point estimation, we always get:► Single valueSolved By Wajid► Two values► Range of values► ZeroQuestion No: 10 ( Marks: 1 ) - Please choose oneThe sample variance2S2 (x x)n is:► Unbiased estimator of 2


► Unbiased estimator of► None of theseQuestion No: 11 ( Marks: 1 ) - Please choose oneVar(4X + 5) =__________► 16 Var (X)► 16 Var (X) + 5

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► 4 Var (X) + 5► 12 Var (X)Question No: 12 ( Marks: 1 ) - Please choose oneWhen f (x, y) is bivariate probability density function of continuous r.v.'s X and Y, then

f x, ydx dy is equal to:► 1► 0► -1► Solved By WajidQuestion No: 13 ( Marks: 1 ) - Please choose oneThearea under a normal curve between 0 and -1.75 is► .0401► .5500► .4599► .9599Question No: 14 ( Marks: 1 ) - Please choose oneWhen a fair die is rolled, the sample space consists of:► 2 outcomes► 6 outcomes► 36 outcomes► 16 outcomesQuestion No: 15 ( Marks: 1 ) - Please choose oneWhen testing for independence in a contingency table with 3 rows and 4 columns, there are________ degrees of freedom.► 5► 6► 7► 12Question No: 16 ( Marks: 1 ) - Please choose oneTheF- test statistic in one-way ANOVA is:► SSW / SSE► MSW / MSE► SSE / SSW► MSE / MSWQuestion No: 17 ( Marks: 1 ) - Please choose oneThe continuity correction factor is used when:► The sample size is at least 5

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► Both nP and n (1-P) are at least 30► A continuous distribution is used to approximate a discrete distribution► The standard normal distribution is appliedQuestion No: 18 ( Marks: 1 ) - Please choose oneSolved By WajidA uniform distribution is defined by:► Its largest and smallest value► Smallest value► Largest value► Mid valueQuestion No: 19 ( Marks: 1 ) - Please choose oneWhich graph is made by plotting the mid point and frequencies?► Frequency polygon► Ogive► Histogram► Frequency curveQuestion No: 20 ( Marks: 1 ) - Please choose oneIn aset of 20 values all the values are 10, what is the value of median?► 2► 5► 10► 20Question No: 21 ( Marks: 1 )If

P X 0=18,

P X 1=38,

P X 2=38andP(X 3)=18Then find F (1)Question No: 22 ( Marks: 2 )

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Write down the formula of mathematical expectation.e=(w * p) + (-v *1). eQuestion No: 23 ( Marks: 3 )Discuss the statistical independence of two discrete random variables:Solved By WajidQuestion No: 24 ( Marks: 3 )Forgiven data calculate the mean and standard deviation of sampling distribution of mean if thesampling is down without replacement.N 1000, n 25, 68.5, 2.7Question No: 25 ( Marks: 3 )Elaborate the Least Significant Difference (LSD) Test.Question No: 26 ( Marks: 3 )Statethe Bayes’ Theorem.Question No: 27 ( Marks: 5 )Themeans and variances of the weekly incomes in rupees of two samples of workers are given in thefollowing table, the samples being randomly drawn from two different factories:Calculate the 90% confidence interval for the real difference in the incomes of the workers fromthe two factories.Question No: 28 ( Marks: 5 )From the given datan 1340, x 723, p .54and 0 0 1 0 H : P 0.5against H : P 0.5.Carry out the significance test for the stated hypothesis.Question No: 29 ( Marks: 5 )Given the Probability density function.Factory Sample Size Mean VarianceA 160 12.80 64B 220 11.25 47 elsewherefor xf xx0,, 0 2 2

Solved By WajidCompute the distribution function F(x).

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Question No: 30 ( Marks: 10 )f(x,y) 1 (6 – x – y), 0 x 2; 2 y 4,80, elsewhere a) Verify that f(x,y) is a jointdensity function.b) Calculate,2,Y 52P X 3 Question No: 31 ( Marks: 10 )Let1 2 3 X , X , Xbe a random sample of size 3 from a population with mean and variance 2

Consider the following two estimators of the mean1 2 311 2 32324T X X XT X X X Which estimator should be preferred?

www.virtualinspire.comMIDTERM EXAMINATIONSTA301- Statistics and ProbabilityQuestion No: 1 (Marks: 1) - Please choose one10! =………….► 362880► 3628800

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► 362280► 362800Question No: 2 (Marks: 1) - Please choose oneIf a player well shuffles the pack of 52 playing cards, then the probability of ablack card from 52 playing cards is:►152►1352►452►2652Question No: 3 (Marks: 1) - Please choose oneThe probability of drawing a ‘jack card ‘from 52 playing cards is:► 152►452►1352►2652Question No: 4 (Marks: 1) - Please choose oneWhich dispersion is used to compare variation of two series?www.virtualinspire.com► C.V.► Q.D.► M.D.► S.D.Question No: 5 (Marks: 1) - Please choose oneIf all the values fall on the same straight line and the line has a positive slopethen what will be the value of the correlation coefficient ‘r’:► 0 ≤ r ≤ 1► r ≥ 0► r = +1► r=-1Question No: 6 (Marks: 1) - Please choose oneIn a regression line Y= a + bX, the value of the correlation coefficient will be zero if:► Intercept a = 0

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► Intercept a ≠ 0► Slope b = 0► Slope b ≠ 0Question No: 7 (Marks: 1) - Please choose oneWhen two coins are tossed the probability of at least one head is:► 1/4► 3/4► 2/4► 4/4Question No: 8 (Marks: 1) - Please choose oneWhich one of the following measurement does not divide a set of observationsinto equal parts?► Quartiles► Deciles► Percentiles► Standard deviationsQuestion No: 9 (Marks: 1) - Please choose oneIn the model Y = mX + a, Y is also known as the:► Predictor variable► Independent variable► Predicted (dependent) variable► Explanatory variablewww.virtualinspire.comQuestion No: 10 (Marks: 1) - Please choose oneAccording to empirical rule approximately 95% of the measurements will fall underwhich interval?► X S► X 2S► X 3S► X 4SQuestion No: 11 (Marks: 1) - Please choose oneWhich one of the following is written at the top of the table?► Source note► Foot note► Prefatory note► TitleQuestion No: 12 (Marks: 1) - Please choose oneIf a curve has a longer tail to the right, it is called:► Positively skewed► Negatively skewed► J-shaped► SymmetricQuestion No: 13 (Marks: 1) - Please choose oneWhich one of the following is the class frequency?► The number of observations in each class► The difference between consecutive lower class limits► Always contains at least 5 observations

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► Usually a multiple of the lower limit of the first classQuestion No: 14 (Marks: 1) - Please choose oneIf X is a discrete random variable, then the functionf (x)is► A probability function► A probability density function► A density function► A distribution functionwww.virtualinspire.comQuestion No: 15 (Marks: 1) - Please choose oneWhich one of the following graphs is used for a time series data?► Histogram► Historigram► Frequency curve► Frequency polygonQuestion No: 16 (Marks: 1) - Please choose oneIf you connect the mid-points of rectangles in a histogram by a series of lines thatalso touches the x-axis from both ends, what will you get?► Ogive► Frequency polygon► Frequency curve► HistorigramQuestion No: 17 (Marks: 1) - Please choose oneIf mean of the two observations is 10.5, then median of these two observations will be:► 7.5► 8.5► 9.5► 10.5Question No: 18 (Marks: 1) - Please choose oneWhich one is the formula of mid range?► m 0 x x► 0 m x x►02m x x►02m x xQuestion No: 19 (Marks: 1) - Please choose oneWhich one of the following is not included in measures of central tendency?► Quartile deviation► Harmonic mean► Geometric mean► Arithmetic mean

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Question No: 20 (Marks: 1) - Please choose oneFor the given data 2, 3, 7, 0, -8 G. M will be:www.virtualinspire.com► Negative► Positive► Zero► UndefinedQuestion No: 21 (Marks: 2)Why measure of central tendency and measure of dispersion are complementary toeach other?Answer: Together both measures give us adequate description of data.Question No: 22 (Marks: 2)What do you know about discrete random variable?Answer:Such a numerical quantity whose value is determined by the value of a randomexperiment is called a random variable.Example: If we toss three dice together and let X represents the number ofheads, then the random variable X consists of the value 0, 1, 2, and 3. the X inthis example is a discrete random variable.Question No: 23 (Marks: 3)What is the subjective approach to the probability?Answer:Subjective probability is a measure of the strength of a person’s belief regarding theoccurrence of an event A. Probability in this sense is purely subjective and is based onwhatever evidence is available to the individual.It has a disadvantage that two or more persons faced with the same evidence may arriveat different probabilities.Example:Suppose a panel of three judges is hearing a trial. It is possible that based on theevidence that is presented; two of them arrive at the conclusion that the accused is guiltywhile one of them decides that the evidence is not strong to draw this conclusion.Question No: 24 (Marks: 3)Explain the difference between absolute dispersion and relative dispersion:Answer:Question No: 25 (Marks: 5)Differentiate between the mutually exclusive events and exhaustive events.www.virtualinspire.comAnswer:Mutually Exclusive Events: Two events A and B of a single experiment are said tobe mutually exclusive if and only if they both can’t occur at the same time.Example:When a die is rolled, the events ‘even number’ and odd number are mutuallyexclusive as we can get either an even number or an odd number in one throw,not both at the same time.Exhaustive Events: Events are said to be collectively exhaustive, when theunion of mutually exclusive events is equal to the entire sample space S.

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Examples:In the coin tossing experiment, head and tail are collectively exhaustive events.Question No: 26 (Marks: 5)Find the first two moments about mean from the following data.X= 3www.virtualinspire.comMIDTERM EXAMINATIONSTA301- Statistics and Probability (Session - 6)Question No: 1 ( Marks: 1 ) - Please choose oneFor a positively skewed distribution m3 will be:► Positive► Negative► Zero► 1Question No: 2 ( Marks: 1 ) - Please choose oneWhen data is labeled to identify an attribute of element, the measurement scale is:► Ordinal► Interval► Nominal► RatioQuestion No: 3 ( Marks: 1 ) - Please choose oneSuppose the estimated equation is has been calculated for a set of data. Whatis slop of the line:► 0www.virtualinspire.com► 2► -2► 5Question No: 4 ( Marks: 1 ) - Please choose oneIf P(B|A) = 0.25 and , then P(A) is:► 0.05► 0.80► 0.95► 0.75Question No: 5 ( Marks: 1 ) - Please choose oneWhich branch of statistics deals with the techniques that are used to organize,summarize, and present the data:► Advance statistics► Probability statistics► Descriptive statistics► Inferential statisticswww.virtualinspire.comQuestion No: 6 ( Marks: 1 ) - Please choose oneIn a sample of 800 students in a university, 160, or 20%, are Business majors. Based onthe above information, the school's paper reported that "20% of all the students at theuniversity are Business majors." This report is an example of :

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► A sample► A population► Sstatistical inference► Descriptive statisticsQuestion No: 7 ( Marks: 1 ) - Please choose oneA set that contains all possible outcomes of a system is known as► Finite Set► Infinite Set► Universal Set► No of theseQuestion No: 8 ( Marks: 1 ) - Please choose oneIf X and Y are independent, then Var(X-Y) is equal to:►www.virtualinspire.com►►► ZeroQuestion No: 9 ( Marks: 1 ) - Please choose oneWhich of the following is the class frequency► The number of observations in each class► The difference between consecutive lower class limits► Always contains at least 5 observations► Usually a multiple of the lower limit of the first classQuestion No: 10 ( Marks: 1 ) - Please choose oneHow to construct the class interval:► Divide the class frequencies in half► Divide the class frequency by the number of observations► Find the difference between consecutive lower class limits► Count the number of observations in the classQuestion No: 11 ( Marks: 1 ) - Please choose oneData in the Population Census Report is:► Ungrouped datawww.virtualinspire.com► Secondary data► Primary data► Arrayed dataQuestion No: 12 ( Marks: 1 ) - Please choose oneWhat is the range of -2,-3,-5,-10 :► -12► 8► -8► 2Question No: 13 ( Marks: 1 ) - Please choose oneThe algebraic sum of deviations from mean is:► Maximum► Minimum

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► Zero► Undefinedwww.virtualinspire.comQuestion No: 14 ( Marks: 1 ) - Please choose oneThe sum of squares of deviations from mean is:► Undefined► Zero► Maximum► MinimumQuestion No: 15 ( Marks: 1 ) - Please choose oneStatistic is a numerical quantity, which is calculated from:► Population► Sample► Data► ObservationsQuestion No: 16 ( Marks: 1 ) - Please choose oneWhich of the following is not based on all the observations?► Arithmetic Mean► Geometric Mean► Harmonic meanwww.virtualinspire.com► ModeQuestion No: 17 ( Marks: 1 )Elaborate the word dispersion.We can say that the degree of scatter of data, usually about an average value, can bethe median.Question No: 18 ( Marks: 1 )Define population.We can define population is the collection of individuals or objects having somecommon measurable characteristics.Question No: 19 ( Marks: 2 )What does mean by the independence of two events:We can define independence of two events are statistically independent if theprobability of their occurring jointly equals the product of their respective probabilities.Independence of two events also know as stochastic independence.Question No: 20 ( Marks: 3 )The reciprocal of the values are0.012, 0.0235, 0.0135www.virtualinspire.comCalculate Harmonic MeanHarmonic mean is 250.037Question No: 21 ( Marks: 5 )The probability that a student passes mathematics is 2/3 and the probability that hepasses English is 4/9. If the probability of passing at least one course is 4/5, what is theprobability that he will pass both courses?Math=2/3

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English=4/9Least one passing probability= 4/5Math + English =2/3+4/9=1.114/5+1.11=1.911Question No: 22 ( Marks: 10 )A pair of dice is thrown, then1) Find the sample space for this experimentSuppose if A and B is the pair of dice then lets try to find out how many result we canfindwww.virtualinspire.com A hit first B Hit first B hit Second A Hit Second Both Hit Equally Both didn't Hit2) Determine the probability of getting the sum 8 on the dice3) Find the probability of getting sum 7 or 114, 70, 42, 54, 40, 68, 56, 38, 36, 72

www.virtualinspire.comMIDTERM EXAMINATIONSTA301- Statistics and Probability (Session - 4)Question No: 1 (Marks: 1) - Please choose one10! =………….► 362880► 3628800► 362280► 362800Question No: 2 (Marks: 1) - Please choose oneIf a player well shuffles the pack of 52 playing cards, then the probability of ablack card from 52 playing cards is:►152►1352►452►2652Question No: 3 (Marks: 1) - Please choose oneThe probability of drawing a ‘jack card ‘from 52 playing cards is:► 1

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52►452►1352►2652Question No: 4 (Marks: 1) - Please choose onewww.virtualinspire.comWhich dispersion is used to compare variation of two series?► C.V.► Q.D.► M.D.► S.D.Question No: 5 (Marks: 1) - Please choose oneIf all the values fall on the same straight line and the line has a positive slopethen what will be the value of the correlation coefficient ‘r’:► 0 ≤ r ≤ 1► r ≥ 0► r = +1► r=-1Question No: 6 (Marks: 1) - Please choose oneIn a regression line Y= a + bX, the value of the correlation coefficient will be zero if:► Intercept a = 0► Intercept a ≠ 0► Slope b = 0► Slope b ≠ 0Question No: 7 (Marks: 1) - Please choose oneWhen two coins are tossed the probability of at least one head is:► 1/4► 3/4► 2/4► 4/4Question No: 8 (Marks: 1) - Please choose oneWhich one of the following measurement does not divide a set of observationsinto equal parts?► Quartiles► Deciles► Percentiles► Standard deviationsQuestion No: 9 (Marks: 1) - Please choose oneIn the model Y = mX + a, Y is also known as the:► Predictor variable► Independent variable

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► Predicted (dependent) variablewww.virtualinspire.com► Explanatory variableQuestion No: 10 (Marks: 1) - Please choose oneAccording to empirical rule approximately 95% of the measurements will fall underwhich interval?► X S► X+ 2S► X 3S► X 4SQuestion No: 11 (Marks: 1) - Please choose oneWhich one of the following is written at the top of the table?► Source note► Foot note► Prefatory note► TitleQuestion No: 12 (Marks: 1) - Please choose oneIf a curve has a longer tail to the right, it is called:► Positively skewed► Negatively skewed► J-shaped► SymmetricQuestion No: 13 (Marks: 1) - Please choose oneWhich one of the following is the class frequency?► The number of observations in each class► The difference between consecutive lower class limits► Always contains at least 5 observations► Usually a multiple of the lower limit of the first classQuestion No: 14 (Marks: 1) - Please choose oneIf X is a discrete random variable, then the functionf (x)is► A probability function► A probability density function► A density function► A distribution functionwww.virtualinspire.comQuestion No: 15 (Marks: 1) - Please choose oneWhich one of the following graphs is used for a time series data?► Histogram► Historigram► Frequency curve► Frequency polygonQuestion No: 16 (Marks: 1) - Please choose oneIf you connect the mid-points of rectangles in a histogram by a series of lines thatalso touches the x-axis from both ends, what will you get?► Ogive

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► Frequency polygon► Frequency curve► HistorigramQuestion No: 17 (Marks: 1) - Please choose oneIf mean of the two observations is 10.5, then median of these two observations will be:► 7.5► 8.5► 9.5► 10.5Question No: 18 (Marks: 1) - Please choose oneWhich one is the formula of mid range?► m 0 x x► 0 m x x►02m x x►02m x xQuestion No: 19 (Marks: 1) - Please choose oneWhich one of the following is not included in measures of central tendency?► Quartile deviation► Harmonic mean► Geometric mean► Arithmetic meanQuestion No: 20 (Marks: 1) - Please choose onewww.virtualinspire.comFor the given data 2, 3, 7, 0, -8 G. M will be:► Negative► Positive► Zero► UndefinedQuestion No: 21 (Marks: 2)Why measure of central tendency and measure of dispersion are complementary toeach other?Answer: Together both measures give us adequate description of data.Question No: 22 (Marks: 2)What do you know about discrete random variable?Answer:Such a numerical quantity whose value is determined by the value of a randomexperiment is called a random variable.Example: If we toss three dice together and let X represents the number ofheads, then the random variable X consists of the value 0, 1, 2, and 3. the X inthis example is a discrete random variable.Question No: 23 (Marks: 3)

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What is the subjective approach to the probability?Answer:Subjective probability is a measure of the strength of a person’s belief regarding theoccurrence of an event A. Probability in this sense is purely subjective and is based onwhatever evidence is available to the individual.It has a disadvantage that two or more persons faced with the same evidence may arriveat different probabilities.Example:Suppose a panel of three judges is hearing a trial. It is possible that based on theevidence that is presented; two of them arrive at the conclusion that the accused is guiltywhile one of them decides that the evidence is not strong to draw this conclusion.Question No: 24 (Marks: 3)Explain the difference between absolute dispersion and relative dispersion:Answer:Question No: 25 (Marks: 5)Differentiate between the mutually exclusive events and exhaustive events.www.virtualinspire.comAnswer:Mutually Exclusive Events: Two events A and B of a single experiment are said tobe mutually exclusive if and only if they both can’t occur at the same time.Example:When a die is rolled, the events ‘even number’ and odd number are mutuallyexclusive as we can get either an even number or an odd number in one throw,not both at the same time.Exhaustive Events: Events are said to be collectively exhaustive, when theunion of mutually exclusive events is equal to the entire sample space S.Examples:In the coin tossing experiment, head and tail are collectively exhaustive events.Question No: 26 (Marks: 5)Find the first two moments about mean from the following data.X= 34, 70, 42, 54, 40, 68, 56, 38, 36, 72

Research Method (STA 630) Success Objectives

1- Hypothesis refers to

A. The outcome of an experiment

B. A conclusion drawn from an experiment

C. A form of bias in which the subject tries to outguess the experimenter

D. A tentative statement about the relationship

2- Statistics is used by researchers to

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A. Analyze the empirical data collected in a study

B. Make their findings sound better

C. Operationally define their variables

D. Ensure the study comes out the way it was intended

3- A literature review requires

A. Planning

B. Good & clear writing

C. Lot of rewriting

D. All of the above

4- A literature review is based on the assumption that

A. Copy from the work of others

B. Knowledge accumulates and learns from the work of others

C. Knowledge disaccumulates

D. None of the above option

5- A theoretical framework

A. Elaborates the r/s among the variables

B. Explains the logic underlying these r/s

C. Describes the nature and direction of the r/s

D. All of the above

6- Which of the following statement is not true?

A. A research proposal is a document that presents a plan for a project

B. A research proposal shows that the researcher is capable of successfully conducting the proposed research project

C. A research proposal is an unorganized and unplanned project

D. A research proposal is just like a research report and written before the research project

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7- Preliminary data collection is a part of the


A. Descriptive research

B. Exploratory research

C. Applied research

D. Explanatory research

8- Conducting surveys is the most common method of generating

A. Primary data

B. Secondary data

C. Qualitative data

D. None of the above

9- After identifying the important variables and establishing the logical reasoning in theoretical framework, the next step in the research process is

A. To conduct surveys

B. To generate the hypothesis

C. To focus group discussions

D. To use experiments in an investigation

10- The appropriate analytical technique is determined by

A. The research design

B. Nature of the data collected

C. Nature of the hypothesis

D. Both A & B

11- Personal interviews conducted in shopping malls are known as:

a. Mall interviewsb. Mall intercept interviewsc. Brief interviewsd. None of the given options

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12-WATS lines provided by long distance telephone service at fixed rates. In this regard, WATS is the abbreviation of:

e. West Africa Theological Seminaryf. Washtenaw Area Transportation Studyg. Wide Area Telecommunications Serviceh. World Air Transport Statistics

13-A list of questions which is handed over to the respondent, who reads the questions and records the answers himself is known as the:

i. Interview schedulej. Questionnairek. Interview guidel. All of the given options

14-One of the most critical stages in the survey research process is:

m. Research designn. Questionnaire designo. Interview designp. Survey design


15-Question that consists of two or more questions joined together is called a:

q. Double barreled questionr. General questions. Accurate questiont. Confusing question

16-The number of questionnaires returned or completed divided by the total number of eligible people who were contacted or asked to participate in the survey is called the:

u. Response ratev. Participation ratew. Inflation ratex. None of the given options

17-To obtain the freest opinion of the respondent, when we ask general question before a specific question then this procedure is called as the:

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y. Research techniquez. Qualitative techniqueaa. Funnel techniquebb. Quantitative technique

18-A small scale trial run of a particular component is known as:

cc. Pilot testingdd. Pre-testingee. Lab experimentsff. Both A & B

18-Field testing of the questionnaire shows that:

gg. Respondents are willing to co-operatehh. Respondents are not willing to co-operateii. Respondents do not like any participationjj. All of the given options

19- Service evaluation of hotels and restaurants can be done by the:

kk. Self-administered questionnairesll. Office assistantmm. Managernn. None of the given options


oo. Self-administered questionnairespp. Office assistantqq. Managerrr. None of the given options

21-Discrete variable is also called……….

A. Categorical variable B. Discontinuous variableC. Both A & B D. None of the above

22-“Officers in my organization have higher than average level of commitment” Such a hypothesis is an example of……….

A. Descriptive HypothesisB. Directional HypothesisC. Relational HypothesisD. All of the above

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23-‘Science’ refers to……….

A. A system for producing knowledge B. The knowledge produced by a systemC. Both A & BD. None of the above

24-Which one of the following is not a characteristic of scientific method?

A. DeterministicResearch Method (STA 630) Success Objectives

B. RationalismC. EmpiricalD. Abstraction

25-The theoretical framework discusses the interrelationships among the……….

A. VariablesB. HypothesisC. ConceptD. Theory

26-………research is based on naturalism.

A. Field researchB. Descriptive researchC. Basic researchD. Applied research

27-Personal interviews conducted in shopping malls are known as………

E. Mall interviewsF. Mall intercept interviewsG. Brief interviewsH. None of the given options

28- ……… is used to obtain the freest opinion of the respondent, by asking general question before a specific question.

I. Research techniqueJ. Qualitative techniqueK. Funnel technique

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L. Quantitative technique

29-In, ___________the interviewer and members jointly control the pace and direction of the interview.

M. Field interviewN. Telephonic interviewO. Both A and BP. None of the given options

30-Randomization of test units is a part of ………

Q. PretestR. PosttestS. MatchingT. Experiment

31- Rationalism is the application of which of the following?

A. Logic and arguments

B. Research solution

C. Reasoning

D. Previous findings

32- On which of the following, scientific knowledge mostly relies?

A. Logical understanding

B. Identification of events

C. Prior knowledge

D. All of the given options

33- Which of the following refers to research supported by measurable

evidence?

A. Opinion

B. Empiricism

C. Speculation

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D. Rationalism

34-Research method is applicable in all of the following fields, EXCEPT;

A. Health care

B. Religion


C. Business

D. Government offices

35- All of the following are true statements about action research, EXCEPT;

A. Data are systematically analyzed

B. Data are collected systematically

C. Results are generalizable

D. Results are used to improve practice

36-Which of the following is characteristic of action research?

A. Variables are tightly controlled

B. Results are generalizable

C. Data are usually qualitative

D. Results demonstrate cause-and-effect relationships

37-If a researcher is studying the effect of using laptops in his classroom to ascertain their merit and worth; he is likely conducting which of the following types of research?

A. Experimental

B. Applied

C. Basic

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D. Evaluation

38- Exploratory research addresses which of the following types of question?

A. If

B. How

C. Why

D. What

39- Which of the following is not the source for getting information for exploratory research?

A. Content analysis

B. Survey

C. Case study

D. Pilot study

40- Which of the following is the main quality of a good theory?

A. A theory that has survived attempts at falsification

B. A theory that is proven to be right

C. A theory that has been disproved

D. A theory that has been falsified

41- A variable that is presumed to cause a change in another variable is known as:

A. Discontinuous variable

B. Dependent variable

C. Independent variable

D. Intervening variable

42- Which of the following is the opposite of a variable?130

A. An extraneous variable

B. A dependent variable

C. A data set

D. A constant

43- Which of the following is not a concept?

A. Leadership

B. Total Quality Management

C. Intelligence Quotient (IQ)

D. Human Resource Management

44- Which of the following can best be described as a categorical variable?

A. Age

B. Annual income

C. Grade point average

D. Religion


45-“Income distribution of employees” in a specific organization is an example of which of following type of variable?


B. Continuous variable

C. Dependent variable

D. Independent variable

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46-“There is no relationship between higher motivation level and higher efficiency” is an example of which type of hypothesis?

A. Alternative

B. Null

C. Co relational

D. Research

47- Which of the following is not a role of hypothesis?

A. Guides the direction of the study

B. Determine feasibility of conducting the study

C. Identifies relevant and irrelevant facts

D. Provides framework for organizing the conclusions

48-Hypothesis test may also be called as:

A. Informal test

B. Significance test

C. Moderating test

D. T-test

49-Which type of review compares how different theories address an issue?

A. Context review

B. Integrated review

C. Theoretical review

D. Methodological review

50-After you locate a source, you should write down all details of the reference, EXCEPT;

A. Volumes

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B. Titles

C. Price

D. Full names of the authors

51- ___________research is based on naturalism.

A. Field research

B. Descriptive research

C. Basic research

D. Applied research

52- Personal interviews conducted in shopping malls are known as_________

A. Mall interviews

B. Mall intercepts interviews

C. Brief interviews

D. None of the given options

53- ____________is used to obtain the freest opinion of the respondent, by asking

general question before a specific question.

A. Research technique

B. Qualitative technique

C. Funnel technique

D. Quantitative technique

54- In, ____________the interviewer and members jointly control the pace and

direction of the interview.

A. Field interview

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B. Telephonic interview

C. Both A and B



55- Randomization of test units is a part of ______________

A. Pretest

B. Posttest

C. Matching

D. Experiment

56- Which one of the following sets is the measure of central tendency?

a. Mean, standard deviation, mode

b. Mean, median, standard deviation

c. Arithmetic mean, median, mode

d. Standard deviation, internal validity, mode

57- Internal validity refers to.

a. Researcher’s degree of confidence.

b. Generalisability

c. Operationalization

d. All of the above

58- How many times the students appear in the research class is the example of _________.

a. Intensity

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b. Space

c. Frequency

d. Direction

59- Time consumed in mall intercept interview is .

a. High

b. Moderate

c. Low

d. Nil

60- Departmental stores selected to test a new merchandising display system is

the example of .

a. Quota sampling

b. Convenience sampling

c. Judgmental sampling

d. Purposive sampling

61- In ___________, the researcher attempts to control and/ or manipulate the variables in

the study.

1. Experiment

2. Hypothesis

3. Theoretical framework

4. Research design

62- In an experimental research study, the primary goal is to isolate and identify the effect

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produced by the ____.

1. Dependent variable

2. Extraneous variable

3. Independent variable

4. Confounding variable

63- A measure is reliable if it provides consistent ___________.

1. Hypothesis

2. Results

3. Procedure

4. Sensitivity

64- The interview in which questions are already prepared is called ________.

1. Telephonic interview

2. Personal interview


3. Unstructured interview

4. Structured interview

65-The numerical description that describe sample may be expected to differ from those

that describe population because of random fluctuations inherent in sampling process.

1. Sampling design

2. Non-probability sampling

3. Sampling error

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4. Probability sampling

66- In ______________ , each population element has a known and equal chance of

selection.

1. Purposive sampling

2. Quota sampling

3. Stratified sampling

4. Simple random sampling

67- ______ is the evidence that the instrument, techniques, or process used to measure

concept does indeed measure the intended concepts.

1. Reliability

2. Replicability

3. Scaling

4. Validity

68- A researcher is interested in studying why the “new math” of the 1960s failed. She interviews several teachers who used the new math during the 1960s. These teachers are considered as:

1. Primary sources

2. Secondary Sources

3. External critics

4. Internal critics

69- Which of the following is NOT true about stratified random sampling?

1. It involves a random selection process from identified subgroups

2. Proportions of groups in the sample must always match their population

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proportions

3. Disproportional stratified random sampling is especially helpful for getting large

enough subgroup samples when subgroup comparisons are to be done

4. Proportional stratified random sampling yields a representative sample

70- Experimental design is the only appropriate design where_________ relationship can

be established.

1. Strong

2. Linear

3. Weak

4. Cause and Effect

71. Discrete variable is also called……….

E. Categorical variable F. Discontinuous variableG. Both A & B H. None of the above

72.“Officers in my organization have higher than average level of commitment”

Such a hypothesis is an example of……….

E. Descriptive HypothesisF. Directional HypothesisG. Relational HypothesisH. All of the above

73.‘Science’ refers to……….

E. A system for producing knowledge Research Method (STA 630) Success Objectives

F. The knowledge produced by a systemG. Both A & BH. None of the above

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74.Which one of the following is not a characteristic of scientific method?

E. DeterministicF. RationalismG. EmpiricalH. Abstraction

73.The theoretical framework discusses the interrelationships among the……….

E. VariablesF. HypothesisG. ConceptH. Theory

74.………research is based on naturalism.

U. Field researchV. Descriptive researchW. Basic researchX. Applied research

75.Personal interviews conducted in shopping malls are known as………

Y. Mall interviewsZ. Mall intercept interviewsAA. Brief interviewsBB. None of the given options

76.……… is used to obtain the freest opinion of the respondent, by asking general question before a specific question.

CC.Research techniqueDD.Qualitative techniqueEE. Funnel techniqueFF. Quantitative technique

77.In, ……… the interviewer and members jointly control the pace and direction of the interview.

GG. Field interviewHH.Telephonic interviewII. Both A and BJJ. None of the given options

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78.Randomization of test units is a part of ………

KK. PretestLL. PosttestMM. MatchingNN.Experiment

79. In ___________, the researcher attempts to control and/ or manipulate the variables in the study.

1. Experiment

2. Hypothesis


4. Research design

80. In an experimental research study, the primary goal is to isolate and identify the effect produced by the ____.





81. A measure is reliable if it provides consistent ___________.


1. Hypothesis

2. Results

3. Procedure

4. Sensitivity

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82. The interview in which questions are already prepared is called ________.





83. The numerical description that describe sample may be expected to differ from those that describe population because of random fluctuations inherent in sampling process.

1. Sampling design


3. Sampling error


84. In ______________ , each population element has a known and equal chance of

selection.


2. Quota sampling



85. ______ is the evidence that the instrument, techniques, or process used to measure concept does indeed measure the intended concepts.

1. Reliability

2. Replicability

3. Scaling

4. Validity

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86. A researcher is interested in studying why the “new math” of the 1960s failed. She interviews several teachers who used the new math during the 1960s. These teachers are considered as:

1. Primary sources


3. External critics

4. Internal critics

87. Which of the following is NOT true about stratified random sampling?



proportions




88. Experimental design is the only appropriate design where_________ relationship can be established.

1. Strong

2. Linear

3. Weak

4. Cause and Effect

89. Rationalism is the application of which of the following?



C. Reasoning

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90. On which of the following, scientific knowledge mostly relies?




C. Prior knowledge


91. Which of the following refers to research supported by measurable

evidence?

A. Opinion

B. Empiricism

C. Speculation

D. Rationalism

92. Research method is applicable in all of the following fields, EXCEPT;

A. Health care

B. Religion

C. Business


93. All of the following are true statements about action research, EXCEPT;



C. Results are generalizable143


94. Which of the following is characteristic of action research?




D. Results demonstrate cause-and-effect relationship

95. If a researcher is studying the effect of using laptops in his classroom to

ascertain their merit and worth, he is likely conducting which of the

following types of research?

A. Experimental

B. Applied

C. Basic

D. Evaluation

96. Exploratory research addresses which of the following types of

question?

A. If

B. How

C. Why

D. What

97. Which of the following is not the source for getting information for

exploratory research?

A. Content analysis

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B. Survey

C. Case study

D. Pilot study

98. Which of the following is the main quality of a good theory?





100. Which of the following is not a concept?

A. Leadership




101. A variable that is presumed to cause a change in another variable is

known as:






102. Which of the following is the opposite of a variable?

A. An extraneous variable145


C. A data set

D. A constant

103. Which of the following can best be described as a categorical

variable?

A. Age

B. Annual income


D. Religion

104. “Income distribution of employees” in a specific organization is an

example of which of following type of variable?





105. “There is no relationship between higher motivation level and higher

efficiency” is an example of which type of hypothesis?

A. Alternative

B. Null

C. Correlational

D. Research

106. Which of the following is not a role of hypothesis?

146





107. Which type of review compares how different theories address an issue?

A. Context review




108. After you locate a source, you should write down all details of the

reference, EXCEPT;

A. Volumes

B. Titles

C. Price


109. What is the primary focus of establishment surveys in this case study?

A. Collect the data through past studies

B. Analyze the literature review

C. Using of quantitative techniques

D. Data collection through mail and Interview

110. Which one of following is generally common in establishment survey and household survey?

A. Cognitive recall147

B. Homogenous respondents

C. Error free

D. Response burden


111. Which one of the following is not of important consideration in establishment survey while designing questionnaires?

A. Response burden

B. Professional terminology

C. Cognitive recall

D. Use of Records

112. Which of the following method of data collection is not discussed in the case study?

A. Questionnaires

B. Interviews

C. Mail survey

D. Observations

113. Which of the following sampling technique is used for Employee Turnover and Job Openings survey?

A. Simple random sampling

B. Cluster sampling

C. Stratified sampling

D. Convenience sampling

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114. Which one of the following is the limitation of establishment survey in this case study?

A. Cost

B. Limited data

C. Unskilled interviewer

D. Small sample size

115. Which of the following is not the part of specific protocol of focus groups in ETJO?

A. Concept and indicators

B. Definition

C. Availability of records

D. Cognitive recall

116. Which of the following is the draw back of pretest interview in ETJO survey?

A. Small simple size

B. Non cooperative response

C. Probing

D. Questionnaire format

117. Which of the following method of data collection is not used in the case study?

A. Questionnaires

B. Focus groups

C. Correlational method

D. Secondary data

118. What is the basic purpose of ETJO survey?

149

A. To assess the feasibility of collecting job-vacancy and turnover data by

occupation

B. To analyze the problem of labor shortage

C. To assess the motivation level of employees

D. To analyze the factor contributing towards employee turnover

119. Which of the following is the basic purpose of pretest interview in this case study?

A. To identified the potential problem

B. To know the sample size

C. To develop the questionnaire

D. To use agency representative

120. Which one of the following sampling type is used in operations test to select the

units?



B. Cluster sampling

C. Quota sampling

D. Judgment sampling

121. Which of the following is the basic purpose of Response analysis survey in the case study?

A. To assess the quality of ETJO survey data

B. To know the sample size of ETJO survey data

C. To develop the questionnaire for ETJO

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D. To use agency representative for ETJO

122. After Operation test, which of the following test findings were suggested by the

researcher?

A. Need of highly skilled and well trained interviewer

B. Sample size should be increased

C. A decent increase in survey budget

D. Focus group should be included

123. In which one of the following stage researcher consult the literature?

A. Operation test

B. Response analysis survey

C. Document design analysis

D. Pretest interviews

124. Which one of the following sampling type is used in Response analysis survey

(RAS)?


B. Cluster sampling

C. Quota sampling

D. Stratified sampling

125. Which one of the following could be helpful for minimizing the bias in this case

study?

A. Cognitive research

B. Focus group

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C. Pretest Interview

D. Response analysis survey

126. Which one of the following is useful in assessing and clarifying concepts and

definitions at the beginning stages of questionnaire?

A. Operation test

B. Document design analysis

C. Focus group


127. Which one of the following can be more helpful than others in order to determine the exact source of measurement errors in establishment survey?

A. Focus group

B. Operation test

C. Response analysis survey

D. Document design analysis

Identify the ‘True’ and ‘False’ statements. (05)

(1)Review of literature shows the incredibility of the body of knowledge and identifies the points at which the researcher made the research area ambiguous and unclear. (False)

(2)The literature survey provides a solid foundation for developing the theoretical framework. (True)

(3)The hypothesis should not only be specific to a place and situation but also these should be narrowed down with respect to its operation. (True )

(4)A cohort analysis is similar to cross-sectional research. (False)


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(5)A literature review does not consider the prior studies, their agreements or disagreements in the field. (False)

Fill in the blanks with appropriate words.

(1)Research hypothesis is formulated by the researcher which suggests the nature of relationship i.e. the direction of relationship.

(2)Correlational hypothesis merely states that the variables occur together and does not imply that one causes the other.

(3)Longitudinal type of research examine feature of any unit at more than one time.

(4)Historical review traces the development of an idea or shows how a particular issue or theory has evolved over time.

(5)Discontinuous variable is also known as discrete/ categorical/ classificatory variable.

6. Validity problems occur when the researcher’s theoretical definition does not

match that of the government agency or organization that collected the

information.

7. Reliability problems occur when official definition or the method of collecting

Information changes over time.

8. Secondary data refer to information gathered by someone other than the

researcher conducting the present study.

9. Experiments are best for topics where the researcher controls a situation and

manipulates an Independent variable.

10. A social indicator is any measure of wellbeing used in policy.

11.Two power bases of scientific knowledge are Empiricism and Rationalism

12.Action research is a type of Applied research

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13.Three types of longitudinal research are time series, panel, and cohort

14.The research proposal is just like a research report, but it is written before the research project begins.

15.Natural science concepts are often expressed in symbolic forms.

16.The double blind experiment is designed to control experimenter expectancy.

17.Pilot testing is also called pre-testing.

18.The totality, out of which sample is drawn is referred to as population.

19.The physical setting of the interview creates Situational bias.

20.Probing is the verbal prompts made by field worker.

Long Questions:

154

Q1. Write any five similarities of Historical-Comparative research and Field

research?

Answer:

1. Both H-C research and field research recognize that the researcher’s point of view

is an avoidable part of research. Both involve interpretation, which introduce the

interpreter’s location in time, place, and world-view.

2. Both field and H-C research examine a great diversity of data. In both the

research becomes immersed in data to gain an emphatic understanding of events

and people.

3. Both field and H-C research often use grounded theory (theory usually emerges

during the process of data collection.)

4. Both field and H-C research involves a type of translation. The researcher’s

meaning system usually differs from that of people he or she studies, but he or she


tries to penetrate and understand their point of view.

5. Both field and H-C research focus on action, process, and sequence and see time

process as essential.

6. Generalization and theory are limited in field and H-C research.

Q2. How quantitative and qualitative techniques are applied in Historical-

Comparative research.

Answer:

Quantitative approach

The quantitative techniques with some minor adjustment can be applied to study the past

or other cultures.155

The researcher can focus on the issue in one society, few societies or multiple

societies.

The researcher can focus on the issue in one time in the past or examine the issue

across many years/periods in the past.

The researcher can focus on the issue in the present or a recent past period.

The researcher’s analysis could be based primarily on quantitative data or

qualitative data.

Qualitative approach

The researcher must be able to take on, mentally, the circumstances, views, and

feelings of those being studied to interpret their action appropriately.

The historical-comparative research must find patterns among the voluminous

details describing the subject matter of study.

Question # 01

How do concrete and abstract concepts differ? Give example.

(Marks: 04)

Solution:

Concrete Concepts:

Concrete ones refer to straightforward physical objects or familiar experiences.

Abstract concepts:

Abstract concepts refer to ideas that have a scattered meaning or an indirect expression Abstraction is a thought process wherein ideas are distanced from objects.

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The difference between concrete and abstract concepts can be expressed with some characterizations like,

1. Abstract concepts have only relational properties while concrete concepts have some fundamental properties.

2. Abstract concepts are universals and concrete concepts are particulars.3. Abstract concepts are sets (generalized) and concrete concepts are individuals

(specified).4. Concrete concepts are known by observation whereas abstract concepts are known

in some other way, e.g., by abstraction, by intuition, etc

Example

Print Media (Abstract)

Publication

News Paper

Daily Dawn (Concrete)

Question # 02


Given the situation below, Discuss with reason into which category they fall

According to the purpose of doing research and The uses of research

(Marks: 03, 03)

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Scenario 1:

Reasons for Absenteeism

A university professor wanted to analyze in depth the reasons for absenteeism of employees in organizations. Fortunately, a company within 20 miles of the campus employed her as a consultant to study that very issue.

Solution:

According to the purpose of doing research :It is Explanatory research as the purpose is to find out the reasons for a phenomenon i.e. absenteeism of employees in organizations. Research seeks to determine the answers to why question about a specific behavior.

According to the uses of research:It is applied research since, the problem is being faced by an organization and the research is called upon to solve it.

Scenario 2:

Effects of Nasal Spray on Flu

A research scientist surveys 1,000 employees in different organizational settings to study the efficacy of several types of nasal sprays in controlling the flu virus. He subsequently publishes his findings in a highly respected medical journal.

Solution:

According to the purpose of doing research :It is Descriptive research, as, the research question only finds out the special effects of several types of nasal sprays in controlling the flu virus in different organizational settings. It is to find out the relationship among the substances under study.

158

According to the uses of research:It is a Basic research since the underlying purpose is to expand the frontier of knowledge

.

Question#01:

Why turn over is high in some organizations?

As per above given query, explain the following components of Theoretical frame work; (Marks: 10)

i) Develop an inventory of variables (min. five variables required)ii) Specify direction of relationshipiii) Give clear explanation why you should expect the proposed relationship

existsiv) Make an inventory of propositions

Ans:

i) Develop an inventory of variables

Salary Package is low, Inflexibility in working hours, Low decentralization (participation in decision making), Lack of other benefits (bonus, appraisals, conveyance facilities, etc), Poor working ambiance

ii) Specify direction of relationship

a) Between salary & turn-over negative relationship existsb) Between flexible working hours & turn-over negative relationship existsc) Between decentralization & turn-over negative relationship exists


d) Between extra benefits & turn-over negative relationship existse) Between ambiance & turn-over negative relationship exists

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iii) Give clear explanation why you should expect the proposed relationship exists?

a) Between salary & turn-over negative relationship exists because in current era a good salary package has more attraction for employees to remain in the same organization. So organizations that keep themselves up-dated with privileged market salary packages usually have low turn over ratio.

b) Between flexible working hours & turn-over negative relationship exists because flexibility in working hours give some relaxation to employees especially in case when their targets are not achieved due to a reason able fact.

c) Between decentralization & turn-over negative relationship exists because participation in decision making raise confidence of employee and motivation level. So, organization have more decentralized system face low turn-over ratio.

d) Between extra benefits & turn-over negative relationship exists. The organizations offer different packages like bonuses, conveyance facilities etc, such organizations have more satisfies employees and low turn over.

e) Between ambiance & turn-over negative relationship exists. Working ambiance does matter a lot. Good ambiance that help in releasing working stress increase the employee motivation and interest in doing job well.

Question#02:

What is meant by a Research Proposal? Explain briefly. Also mention at what time a research proposal is submitted? (Marks: 05)

Note: (Copied data from hand outs will not be appreciated)

Ans:

A research proposal is a document that plans how and in which manner a research will be conducted. Research proposals contain extensive literature reviews. Such proposals must offer convincing support for your research topic. It means the topic/issue for which research study is being proposed should be sound enough to conduct a worthy research. The proposal must describe a detailed methodology for conducting the research i.e. which tools are going to be used in your research.

More over when writing a proposal it is well to assume that reader of your proposal is interested to find out the answer of these questions;

What do you want to do, how much will it cost, and how much time will it take?

What has already been done in the area of your project?

160

How do you plan to do it? How will the results be evaluated?

A good proposal is that which well defines these questions and convinces the reader that research on specified issue is needed to conduct. So, the research proposal is submitted before starting the research project because in this you plan how the data will be collected and analyzed.

Q. Explain the difference between these terms with one example of each.

i. Population and target population

ii. Sampling unit and observation unit

iii. Parameter and statistic

i. Population and Target Population.

Population refers to the entire group of people, events or things of interest that the

researcher wishes to investigate.

Target population is the complete group of specific population elements relevant to the

research project.

Example

Suppose a researcher wants to investigate the productivity of employees working in

multinationals in Pakistan.

All the employees working in multinational will be the population.

The researcher wants to investigate the productivity of employees working in

multinational in FMCG sector in Pakistan.


All the employees working in multinationals in FMCG sector in Pakistan will be the

target population.

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ii. Sampling Unit and Observation Unit

A sampling unit is that element or set of elements considered for selection in some stage

of sampling.

An observation unit is an element or aggregation of elements from which the

information is collected.

Example

In the above example the researcher selects employees from three FMCG multinationals

(Procter and Gamble, Unilever and Nestle) for data collection. Among these employees

he selected First Line Managers for collecting the data. Among all First Line Manager he

selects 40 Line managers for data collection.

In this example the employees from three FMCGs (Procter and Gamble, Unilever and

Nestle) are the primary sampling unit, all the First Line managers are the secondary/ final

sampling unit and the selected First Line managers are the observation unit.

iii. Parameter and Statistics

A parameter is the summary description of a given variable in a population while

Statistic is the summary description of a given variable in a survey sample.

Example

In the above example the mean productivity of all the employees working in the

multinational is the Parameter and the mean productivity of the First Line managers from

those the researcher collected the data is the Statistics.

162

Q: Define Research? Discuss the special features of Scientific method of Research?

Solution:

Definition of Research:

Research is an organized and systematic way of finding answers to questions by gathering the needed information. General image of the research is that it has something to do with the laboratory where scientists are supposedly doing some experiments. Research is simply the process of finding solutions to a problem after thorough study and analysis of the situational factors. In research, we try to follow a system or a procedure in an organized manner. It is all the more necessary in case we want to repeat the study, or somebody else wants to verify our findings. In the latter case the other person has to follow the same procedure that we followed. Hence not only we have to do the study in a systematic manner but also that system should be known to others.

Special Features of Scientific Method of Research:

The Scientific method of Research is a procedure to produce knowledge and to discover the principles & laws in this universe.

Special Features of Scientific Method of Research are as follows:

1. Empirical

Scientific method is concerned with the realities that are observable through “sensory experiences.” It generates knowledge which is verifiable by experience or observation. Some of the realities could be directly observed, like the number of students present in the class and how many of them are male and how many female. The same students have attitudes, values, motivations, aspirations, and commitments. These are also realities which cannot be observed directly, but the researchers have designed ways to observe these indirectly. Any reality that cannot be put to “sensory experience” directly or indirectly (existence of heaven, the Day of Judgment, life hereafter, God’s rewards for good deeds) does not fall within the domain of scientific method.

2. Verifiable

Observations made through scientific method are to be verified again by using the senses to confirm or refute the previous findings. Such confirmations may have to be made by the same researcher or others. We will place more faith and credence in those findings and conclusions if similar findings emerge on the basis of data collected by other researchers using the same methods. To the extent that it does happen (i.e. the results are replicated or repeated) we will gain confidence in the scientific nature

163

of our research. Replicability, in this way, is an important characteristic of scientific method. Hence revelations and intuitions are out of the domain of scientific method.

3. Cumulative

Prior to the start of any study the researchers try to scan through the literature and see that their study is not a repetition in ignorance. Instead of reinventing the wheel the researchers take stock of the existing body of knowledge and try to build on it. Also the researchers do


not leave their research findings into scattered bits and pieces. Facts and figures are to be provided with language and thereby inferences drawn. The results are to be organized and systematized. Nevertheless, we don’t want to leave our studies as stand alone. A linkage between the present and the previous body of knowledge has to be established, and that is how the knowledge accumulates.

4. Deterministic

Science is based on the assumption that all events have antecedent causes that are subject to identification and logical understanding. For the scientist, nothing “just happens” – it happens for a reason. The scientific researchers try to explain the emerging phenomenon by identifying its causes. Of the identified causes which ones can be the most important? For example, in the 2006 BA/BS examination of the Punjab University 67 percent of the students failed. What could be the determinants of such a mass failure of students? The researcher may try to explain this phenomenon and come up with variety of reasons which may pertain to students, teachers, administration, curriculum, books, examination system, and so on. Looking into such a large number of reasons may be highly cumbersome model for problem solution. It might be appropriate to tell, of all these factors which one is the most important. The researcher tries to narrow down the number of reasons in such a way that some action could taken.

5. Ethical and Ideological Neutrality

The conclusions drawn through interpretation of the results of data analysis should be objective; that is, they should be based on the facts of the findings derived from actual data, and not on our own subjective or emotional values. For instance, if we had a hypothesis that stated that greater participation in decision making will increase organizational commitment, and this was not supported by the results, it makes no sense if the researcher continues to argue that increased opportunities for employee participation would still help. Such an argument would be based, not on the factual, data based research findings, but on the subjective opinion of the researcher. If this

164

was the conviction of the researcher all along, then there was no need to do the research in the first place. Researchers are human beings, having individual ideologies, religious affiliations, cultural differences which can influence the research findings. Any interference of their personal likings and dis-likings in their research can contaminate the purity of the data, which ultimately can affect the predictions made by the researcher. Therefore, one of the important characteristics of scientific method is to follow the principle of objectivity, uphold neutrality, and present the results in an unbiased manner.

6. Statistical Generalization

Generalisability refers to the scope of the research findings in one organizational setting to other settings. Obviously, the wider the range of applicability of the solutions generated by research, the more useful the research is to users. For instance, if a researcher’s findings that participation in decision making enhances organizational commitment are found to be true in a variety of manufacturing, industrial, and service organizations, and not merely in the particular organization studied by the researcher, the generalisability of the findings to other organizational settings is enhanced. The more generalizable the research, the greater its usefulness and value.

For wider generalisability, the research sampling design has to be logically developed. Here the use of statistics is very helpful. Statistics is device for comparing what is observed and what is logically expected. The use of statistics becomes helpful in making generalizations, which is one of the goals of scientific method.

7. Rationalism

Science is fundamentally a rational activity, and the scientific explanation must make sense. Religion may rest on revelations, custom, or traditions, gambling on faith, but science must rest on logical reason. There are two distinct logical systems important to the scientific quest, referred to as deductive logic and inductive logic.

Q: Define Hypothesis? What are different types of hypothesis? Explain.

Solution:

Definition of Hypothesis:

A proposition that can be verified to determine its reality is a hypothesis. A hypothesis may be defined as a logically conjectured relationship between two or more variables, expressed in the form of a testable statement. Relationship is proposed by using a strong logical argumentation. This logical relationship may be part of theoretical framework of the study.

165

For example,

Officers in my organization have higher than average level of commitment (variable).

Level of job commitment of the officers is associated with their level of efficiency. Level of job commitment of the officers is positively associated with their level of

efficiency.Research Method (STA 630) Success Objectives

The higher the level of job commitment of the officers the lower their level of absenteeism.

Types of Hypothesis:

There are different types of hypothesis which are as follows.

1-Descriptive Hypothesis

Descriptive hypothesis contains only one variable thereby it is also called as univariate hypothesis. Descriptive hypotheses typically state the existence, size, form, or distribution of some variable. The first hypothesis contains only one variable. It only shows the distribution of the level of commitment among the officers of the organization which is higher than average. Such a hypothesis is an example of a Descriptive Hypothesis.

2- Relational Hypothesis

These are the propositions that describe a relationship between two variables. The relationship could be non-directional or directional, positive or negative, causal or simply correlational.

While stating the relationship between the two variables, if the terms of positive, negative, more than, or less than are used then such hypotheses are directional because the direction of the relationship between the variables (positive/negative) has been indicated. These hypotheses are relational as well as directional. The directional hypothesis is the one in which the direction of the relationship has been specified.

Non-directional hypothesis is the one in which the direction of the association has not been specified. The relationship may be very strong but whether it is positive or negative has not been postulated.

Correlational hypotheses state merely that the variables occur together in some specified manner without implying that one causes the other. Such weak claims are often made when we believe that there are more basic causal forces that affect both variables. For example:

166

Level of job commitment of the officers is positively associated with their level of efficiency.

Explanatory (causal) hypotheses imply the existence of, or a change in, one variable causes or leads to a change in the other variable. This brings in the notions of independent and the dependent variables. Cause means to “help make happen.” So the independent variable may not be the sole reason for the existence of, or change in the dependent variable.

3- Null Hypothesis

It is used for testing the hypothesis formulated by the researcher. Researchers treat evidence that supports a hypothesis differently from the evidence that opposes it. They give negative evidence more importance than to the positive one. It is because the negative evidence tarnishes the hypothesis. It shows that the predictions made by the hypothesis are wrong. The null hypothesis simply states that there is no relationship between the variables or the relationship between the variables is “zero.” That is how symbolically null hypothesis is denoted as “H0”. For example:

H0 = There is no relationship between the level of job commitment and the level of efficiency. Or

H0 = The relationship between level of job commitment and the level of efficiency is zero. Or the two variables are independent of each other.

It does not take into consideration the direction of association (i.e. H0 is non directional), which may be a second step in testing the hypothesis.

4- Alternative Hypothesis

The alternative (to the null) hypothesis simply states that there is a relationship between the variables under study. In our example it could be: there is a relationship between the level of job commitment and the level of efficiency. Not only there is an association between the two variables under study but also the relationship is perfect which is indicated by the number “1”. Thereby the alternative hypothesis is symbolically denoted as “H1”. It can be written like this:

H1: There is a relationship between the level of job commitment of the officers and their level of efficiency.

5- Research Hypothesis

Research hypothesis is the actual hypothesis formulated by the researcher which may also suggest the nature of relationship i.e. the direction of relationship. In our example it could be:

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Q: Ahmad is the manager of a restaurant; he wants to see his staff cooperative and hardworking but his staff is not working well according to his will. He decided to give the incentives in order to motivate and encourage them but his policy did not work effectively. There can be many factors behind this behavior of staff that needs to be researched. For this purpose, he appoints you as a researcher and asks you to discover those factors and submit a report to him. How you will undertake this kind of


research and what steps you will choose to make a report about the behavior of the staff?

Solution:

The manager of the restaurant appoints me as a researcher to find out the factors behind the staff behavior. I will take the following steps in order to undertake this research and to make a report. These steps are as follows:

STEP 1: To Select the topic of research:

First of all I will select the topic which is a general area of study or issue. The topic in this research is the factors behind the staff behavior. A topic appears to be too broad for conducting research. The specific issues that need to be researched within the situation may not be identified at this stage. I will try to analyze the problems currently existing in the restaurant that needs to be solved and the areas that a manager believes need to be improved in the restaurant (improving the existing policies). Then I will develop some research questions that a basic researcher wants to answer empirically.

STEP 2: Preliminary Data Collection or to Explore different areas from where I can get information related to the restaurant and staff behavior:

After selecting the topic, I will collect data from different sources. This step may be considered as part of the exploratory research. An exploration typically begins with a search for published data and studies. Such sources can provide secondary data which becomes part of the background information (about the restaurant & groups of people). Some secondary sources of data are statistical bulletins, government publications, information published or unpublished, case studies, online data, web

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sites, and the Internet from where I can get information. In addition, information can also be collected from the people who are well informed about the staff and restaurant, especially those who have clearly stated positions on controversial aspects of the problem. In certain situations, I will also focus on group discussions with the staff of the restaurant. Such discussions can help me in the identification of factors and having clarification of their behavior.

STEP 3: Problem Definition

After having discussions with the professionals as well as with the staff to whom the issue relates, and the review of literature, now I will be in a position to narrow down from its original broad base and define the factors clearly. Translate the broad issue into a research question. As part of the applied research convert the management dilemma into a management question, and then on to research question that fits the need to resolve the dilemma. The symptoms of a problem might help tracing the real problem. For example in this research, the productivity decline of workers is an issue. The manager has tried to solve it by the provision of incentives but his policy did not work. I will find the possible factors like the morale and motivation of the workers having some other antecedents.

STEP 4: To develop the Theoretical Framework

Consultations with the informants and professionals, and the review of literature will help me in the identification of different factors that are considered to be relevant. Now I will need to make a logical relationship among several factors identified. This will help in the delineation of the theoretical framework. The theoretical framework discusses the interrelationships among the variables that are deemed to be integral to the dynamics of the situation being investigated. Developing such a conceptual framework helps to postulate or hypothesize and test certain relationships.

STEP 5: To Generate the Hypotheses

Once I have identified the important variables relevant to an issue and established the logical reasoning in the theoretical framework, I will be in a position to test whether the relationships that have been theorized do in fact hold true. By testing these relationships scientifically, I will obtain reliable information to determine the relationship among the variables. The results of these tests offer part of the answers to the formulated research questions, whether these relate basic research or to applied research.

STEP 6: To make a Research Design

Research design is a master plan specifying the methods and procedures for collecting and analyzing the needed information. It is a framework or the blueprint that plans the action for research project. The objectives of the study determined during the

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early stages of the research are included in the design to ensure that the information collected is appropriate for solving the problem. It is very important to specify the sources of information, and the research method or technique (survey or experiment, for example) to be followed in the study. Broadly there are six basic research methods for descriptive and causal research: surveys, experiments, observation, communication analysis (content analysis), case study, focus group discussion.

STEP 7: Data Collection, Data Processing, and Analysis


Data collection is integral part of the research design; Data collection is determined by the research technique selected for the project. Data can be collected in a variety of ways, in different settings – field or lab – and from different sources. It could include interviews – face to face interviews, telephone interviews, computer-assisted interviews, and interviews through electronic media; questionnaires that either personally administered, sent through mail, or electronically administered; observation of individuals and events which could be participant or non participant. Once the fieldwork has been completed, the data must be converted into a format that will answer the research questions and help testing the hypotheses. The computer can help in making tables and the application of different statistics.

STEP 8: Testing the Hypotheses; Answering the Research Questions

The analysis and interpretation of the data shall be the means to testing the formulated hypotheses as well as finding answers to the research questions. In case of applied research, the research should be helpful in finding solutions to the problems of the organization or society. Making recommendations may also be part of this process.

STEP 9: Report Writing

The research report should communicate the research findings effectively. All too often the report is a complicated statement of the study’s technical aspects and sophisticated research methods. The report has to be presented in the format as it may have been part of the terms of reference if it is a sponsored study. I will write the basic factors behind the staff behavior in my report and I will also give some suggestions to the manager to motivate the staff so that they can work efficiently.

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Q: Define the measure that is used by the researcher in order to capture the intensity, direction, level, or potency of a variable construct. Also describes the different types of that measure.

Solution:

The measure that is used by the researcher in order to capture the intensity, direction, level, or potency of a variable construct:

A scale is a measure in which a researcher captures the intensity, direction, level, or potency of a variable construct. It arranges responses or observations on a continuum or in series of categories. A scale can use a single indicator or multiple indicators.

An index is a measure in which a researcher adds or combines several distinct indicators of a construct into a single score. The composite scores is often a simple sum of the multiple indicators. Indexes are often measured at the interval or ratio level.

Researchers sometimes combine the features of scales and indexes in a single measure. This is common when a researcher has a several indicators that are scales (i.e. that measure intensity or direction). The researcher then adds these indicators together to yield a single score, thereby creating an index.

The different types of that measure:

A scale refers to any series of items that are arranged progressively according to value or magnitude, into which an item can be placed according to its quantification. In other words, a scale is a continuous spectrum or series of categories.

It is traditional to classify scales of measurement on the basis of the mathematical comparisons that are allowable with these scales. Four types of scales are nominal, ordinal, interval, and ratio.

Nominal Scale

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A nominal scale is the one in which the numbers or letters assigned to objects serve as labels for identification or classification. This measurement scale is the simplest type. With nominal data, we are collecting information on a variable that naturally or by design can be grouped into two or more categories that are mutually exclusive, and collectively exhaustive.

Nominal scales are the least powerful of the four scales. They suggest no order or distance relationship and have no arithmetic origin. Nevertheless, if no other scale can be used, one can almost always one set of properties into a set of equivalent classes.

Ordinal Scale


Ordinal scales include the characteristics of the nominal scale plus an indicator of order. If a is greater than b and b is greater than c, then a is greater than c. The use of ordinal scale implies a statement of “greater than” or “less than” without stating how much greater or less. Other descriptors can be: “superior to,” “happier than,” “poorer than,” or “above.”

Interval Scale

Interval scales have the power of nominal and ordinal scales plus one additional strength: they incorporate the concept of equality of interval (the distance between 1 and 2 equals the distance between 2 and 3). For example, the elapsed time between 3 and 6 A. M. equals the time between 4 and 7 A. M. One cannot say, however, 6 A.M. is twice as late as 3 A.M. because “zero time” is an arbitrary origin. In the consumer price index, if the base year is 1983, the price level during 1983 will be set arbitrarily as 100. Although this is an equal interval measurement scale, the zero point is arbitrary.

Ratio Scale

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Ratio scales incorporate all the powers of the previous scales plus the provision for absolute zero or origin. Ratio data represent the actual amounts of variable. Measures of physical dimensions such as weight, height, distance, and area are the examples. The absolute zero represents a point on the scale where there is an absence of the given attribute. If we hear that a person has zero amount of money, we understand the zero value of the amount.

Q: (a) Define the Probability & non-Probability sampling.

Solution (a):

Probability Sampling:

In probability sampling, every element in the population has a known nonzero probability of selection. The simple random is the best known probability sample, in which each member of the population has an equal probability of being selected.

Non-Probability Sampling:

In non-probability sampling the probability of any particular element of the population being chosen is unknown. The selection of units in non-probability sampling is quite arbitrary, as researchers rely heavily on personal judgment.

(b) “Snowball sampling is also known as network, chain referral or reputational sampling.” Comment on this statement.

Solution (b):

Snowball sampling:

Snowball sampling is also called network, chain referral, or reputational sampling. It is a method for identifying and sampling cases in the network. It is based on an analogy to a snowball, which begins small but becomes larger as it is rolled on wet snow and picks up additional snow. It begins with one or a few people or cases and spreads out on the basis of links to the initial cases.

This design has been found quite useful where respondents are difficult to identify and are best located through referral networks. In the initial stage of snowball sampling, individuals are discovered and may or may not be selected through probability methods. This group is then used to locate others who possess similar

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characteristics and who, in turn, identify others. The “snowball” gather subjects as it rolls along.

Example:

For example, a researcher examines friendship networks among teenagers in a community. He or she begins with three teenagers who do not know each other. Each teen names four close friends. The researcher then goes to the four friends and asks each to name four close friends, then goes to those four and does the same thing again, and so forth. Before long, a large number of people are involved. Each person in the sample is directly or indirectly tied to the original teenagers, and several people may have named the same person. The researcher eventually stops, either because no new names are given, indicating a closed network, or because the network is so large that it is at thee limit of what he or she can study.

(c)The purpose of cluster sampling is to sample economically while retaining the characteristics of a probability sample. At the same time, cluster sampling addresses two major problems. Discuss those problems.


Solution (c):

The purpose of cluster sampling is to sample economically while retaining the characteristics of a probability sample. At the same time, Cluster sampling addresses following two problems:

1. Researchers lack a good sampling frame for a dispersed population and the cost to reach a sampled element is very high. A cluster is unit that contains final sampling elements but can be treated temporarily as a sampling element itself. A researcher first samples cluster, each of which contains elements, then draws a second sample from within the clusters selected in the first stage of sampling. In other words, the researcher randomly samples clusters, and then randomly samples elements from within the selected clusters. He or she can create a good sampling frame of clusters, even if it is impossible to create one for sampling elements. Once the researcher gets a sample of clusters, creating a sampling frame for elements within each cluster becomes more manageable.

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2. A second advantage for geographically dispersed populations is that elements within each cluster are physically closer to each other. This may produce a savings in locating or reaching each element.

Q: Briefly discuss the steps that are involved in conducting an experiment.

Solution:

Steps in Conducting an Experiment

Broadly there are about 12 steps in conducting an experiment, which are as below:

1. Make a hypothesis that is appropriate for experimental research.2. Decide about an experimental design that will test the hypothesis within practical

limitations. 3. Decide how to create a situation that induces the independent variable.4. Develop a valid and reliable measure of the dependent variable.5. Set up an experimental setting and conduct a pilot test of the treatment and

dependent variable measures.6. Locate appropriate subjects or cases.7. Randomly assign subjects to groups and give careful instructions.8. Gather data for the pretest measure of the dependent variable for all groups.9. Introduce the treatment to the experimental group only (or to the relevant groups if

there are multiple experimental groups) and monitor all groups.10. Gather data for posttest measure of the dependent variable.11. Debrief the subjects by informing them of the true purpose and reasons for the

experiment. Ask subjects what they thought was occurring. 12. Examine data collected and make comparisons between different groups. Where

appropriate, use statistics and graphs to determine whether or not the hypothesis is supported.

Q. Classify this research on the basis of:

i. Purpose of doing research.ii. The use of researchiii. Time dimension in researchJustify your answer.

Answer:

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i. It is an exploratory research. Because it was a new issue and no research was made on it before. The researchers had limited amount of information on this issue and this research provided bases for many other studies.

ii. It is a basic research because it provides knowledge generated to understand a phenomenon of interest to the researcher.

iii. It is a longitudinal research because it examines the employees at more than one time. The research is spread upon 1927 to 1932. A group of 6 women was selected for 5 years so it can be further classified as Panel study.


Q. Identify these variables used in the experiment:

i. Dependent variablesii. Independent variablesiii. Extraneous variables

Justify your answer.

Answer:

i. The variable that is the result of another variable(s) is called a dependent variable. Productivity of the employees is the dependent variable in this case. Because it depends on many other independent variables.

ii. The variable that causes the dependent variable is called independent variable. It is a cause variable. In our example light illumination, rest breaks, duration of work hours, temperature, food, wages and humidity are independent variables because they affect productivity.

iii. Extraneous variables are factors other than the independent variable that could result in changes in the dependent variable. In an experiment, these factors should be controlled so that they are constant in all conditions. If they are not well-controlled, then they result in possible alternative explanations (other than changes in the independent variable) that could account for the changes observed in the dependent variable. Possible extraneous variables in this research can be knowledge of the employees that they are being observed (when employees know that they are being watched, they tend to modify their behavior), special attention paid to them, supervisor’s style, etc.

Q: What do you understand by the term “concepts are an abstraction of reality”? Explain with the help of an example.

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Answer: Concepts are the terms and terminologies used by researchers as means of communication. They are expressed in words, letters, signs and symbols that refer to various events or objects. Abstraction simply means “generalization.” In research methods, we use this term “concepts are an abstraction of reality”. It means that we pick up concepts from observed reality and goes on to the abstraction level. It is a level at which objects and events are expressed in more generalized form.

For example Toyota is a concept, its abstraction is a car and its further abstraction would be motor vehicles. We have changed the simple concept (Toyota) into an abstraction (motor vehicles) which is a more generalized term.

Q: Join the options in column A with appropriate options given in column B. Identify the variables and give reasons for your choice.

Column A Column B

(a) Two men and three women were seriously injured in a road accident 25 km away from Lahore.

(i) Intervening variable

(b) Out break of Malaria in the city increased the consumption of mosquito repellents.

(ii) Independent and dependent variable

(c) Distance learning system increased the literacy level in the country.

(iii)Continuous and discontinuous variable

Answer:

Column A Column B

(a) (iii)

(b) (ii)

(c) (i)


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Identification of Variables:

(a) Men and Women are the example of discontinuous variables and the distance of 25 km is an example of continuous variable.

(b) ‘Out break of malaria’ is the independent variable and ‘increase in the purchase of mosquito repellents’ is dependent variable.

(c) There is a clear indication of many intervening variable such as flexible timing, low fees, low transportation cost, easy access to get education especially for far off areas.

Reasons:

(a) Discontinuous variable has limited number of distinct values which can not be divided into fractions, so male/female or men/women are discontinuous variables. Continuous variable can take infinite number of values and can be divided into fractions, so the distance is continuous variable as it can take any value e.g. 35km, 55.5 km etc.

(b) Independent variables are those variables which identifies forces or conditions that act on something. Malaria is the independent variable as it is causing change in other variable. Dependent variables are the effect or result of another variable. Their occurrence is dependent upon the occurrence of another variable. Increase in the consumption of mosquito repellents is an outcome of increasingly spreading Malaria disease.

(c) Intervening variables are those variables that come between independent and dependent variables and shows a link or mechanism between them. Distance learning (independent variable) has increased the literacy level (dependent variable) and there are other intervening variables which are supporting this relationship e.g. flexible timing, low fees, low transportation cost, easy access to get education especially for far off areas.

Made by Armaan [email protected] 301 all quiz lec 1 to 45Date 20/dec/2009to29/dec/2010Mr. super .Cool1. A quantity obtained by applying certain rule or formula is known asSelect correct option:EstimateEstimator2. Criteria to check a point estimator to be good involvesSelect correct option:ConsistencyUnbiasednessEfficiencyAbove all pg 2583. The F-distribution always ranges from:Select correct option:

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0 to 10 to -8-8 to +80 to +84. 1-a is the probability of ......Select correct option:Type 1 errorRejection regionAcceptance regionType 2 error5. Parameter is a ………quantity.Select correct option:ConstantVariable6. To find the estimate of a parameter…….methods are used.Select correct option:TwoThreeFourMany7. A failing student is passed by an examiner. It is an example of:Select correct option:Type I errorType II errorCorrect decisionNo information regarding student exams8. For two mutually exclusive events A and B, P (A) = 0.2 and P (B) = 0.4, then P(AUB) is:Select correct option:0.80.20.60.5P(AUB)=P(A)+p(B)=0.2+0.4=0.69. An urn contains 4 red balls and 6 green balls. A sample of 4 balls is selected from the urnwithout replacement. It is the example of:Select correct option:Binomial distributionHypergrometric distributionPoisson distributionExponential distribution10. A standard deck of 52 cards is shuffled. What is the probability of choosing the 5 of diamonds:Select correct option:1/51/135/52

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1/5211. If P(AnB) = 0.12 P (A) = 0.3, find P (B) where ‘A’ and ‘B’ are independent:Select correct option:0.10.20.30.40.3X0.4=0.1212. The mean deviation of the normal distribution is approximately:Select correct option:7/8 of the S.D4/5 of the S.D3/4 of the S.D1/2 of the S.D13. We use the Poisson approximation to the binomial when:Select correct option:p is 0.01 or less & n is 10 or morep is 0.05 or less & n is 20 or more pg221p is 0.04 or less & n is 15 or morep is 0.02 or less & n is 10 or more14. The conditional probability P (A\B) is:Select correct option:P(A n B)/P(B) pg157P(A n B)/P(A)P(A U B)/P(B)P(A U B)/P(A)15. We use the General Rule of Multiplication to combine:Select correct option:Events those are not independentMutually exclusive eventsEvents that total more than 1.00Events based on subjective probabilities16. Which statement is NOT CORRECT?Select correct option:The sample standard deviation measures variability of our sample valuesA larger sample will give answers that vary less from the true value than smaller samplesThe sampling distribution describes how our estimate (answer) will vary if a new sample is takenA large sample size always gives unbiased estimators regardless of how the sample is chosen17. Probability of an impossible event is always:Select correct option:Less than oneGreater than oneBetween one and zeroZero18. The number of parameters in uniform distribution is (are):

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Select correct option:12pg 2243419. The probability can never be:Select correct option:1 1/21 -1/220. The conditional probability P (A\B) is:Select correct option:P(A n B)/P(B)P(A n B)/P(A)P(A U B)/P(B)P(A U B)/P(A)21. A random sample of n=25 values gives sample mean 83. Can this sample be regarded as drawnfrom a normal population with μ= 80 and s= 7? In this question the alternative hypothesis willbe:Select correct option:H1: μ = 80H1: μ ? 80H1: μ > 80H1: μ <80 pg 27822. If f(x) is a continuous probability function, then P(X = 2) is:Select correct option:10 1/2223. The binomial distribution is negatively skewed when:Select correct option:p>q pg 214p<qp=qp=q=1/224. If we roll three fair dices then the total number of outcomes is:Select correct option:6 3621612966^3=21625. When we draw the sample with replacement, the probability distribution to be used is:Select correct option:BinomialHypergeometricBinomial & hypergeometric pg 219Poisson

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26. The moment ratios of normal distribution come out to be:Select correct option:0 and 10 and 20 and 3 pg 2260 and 427. The probability of an event is always:Select correct option:greater than 0less than 1between o and 1greater than 128. Symbolically, a conditional probability is:Select correct option:P(AB)P(A/B)P(A)P(AUB)29. Suppose the test scores of 600 students are normally distributed with a mean of 76 andstandard deviation of 8. The number of students scoring between 70 and 82 is:Select correct option:27216426032830. If P (A) = 0.3 and P (B) = 0.5, find P (A/B) where ‘A’ and ‘B’ are independent:Select correct option:0.30.50.80.1531. An urn contains 4 red balls and 6 green balls. A sample of 4 balls is selected from the urnwithout replacement. It is the example of:Select correct option:Binomial distributionHypergrometric distributionPoisson distributionExponential distribution32. If the second moment ratio is less than 3 the distribution will be:Select correct option:MesokurticLeptokurticPlatykurtic pg 226None of these33. For the independent events A and B if P (A) = 0.25, P (B) =0.40 then P (A and B) =……

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Select correct option:0.650.10.500.15P(A)*P(B)0.25*0.40=0.134. A set of possible values that a random variable can assume and their associated probabilities ofoccurrence are referred to as __________.Select correct option:Probability distributionThe expected returnThe standard deviationCoefficient of variation35. A random variable X has a probability distribution as follows: X | 0 1 2 3 P(X) | 2k 3k 13k 2kWhat is the possible value of k:Select correct option:0.010.030.050.0736. The probability of drawing any one spade card is:Select correct option:1/524/5213/5252/5237. The function abbreviated to d.f. is also called the......Select correct option:Probability density functionProbability distribution function pg 172Commutative distribution functionDiscrete function38. Binomial distribution is skewed to the right if:Select correct option:p=qP<qp>qp=n39. A discrete probability function f(x) is always:Select correct option:ZeroOne pg 172NegativeNon-negative40. For a binomial distribution, n= 10 & q= 0.6, the mean of the distribution is:Select correct option:

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0.66.0104P=1-q1-0.6=0.4,mean =np10*0.4=441. In the FA examination, 24candidates offered Statistics. If the probability of passing the subjectbe 1/3, what will be the mean of the distribution?Select correct option:786542. The probability that a certain machine will produce a defective item is 1/4. If a random sampleof 6 items is taken from the output of this machine, what is the probability that there will be 5or more defectives in the sample?Select correct option:3/409618/409619/40964/409643. Probability of type II error isSelect correct option:aB pg 2761-a1-B44. If the values of variables are increasing or decreasing in the same direction then such kind ofcorrelation is referred asSelect correct option:Zero CorrelationPerfect CorrelationPositive CorrelationNegative Correlation45. The moving averages of the Prices 55,60,65,70 areSelect correct option:70, 7560, 6565,6570,6046. The best measure of variation isSelect correct option:RangeQuartile deviationVarianceCoefficient of variance

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47. Ms. Christian calculated a correlation coefficient of .75. Which of the following reflects thebest interpretation of this?Select correct option:Weak negative.Strong negative.Weak positive.Strong positive.48. ………use the division of a circle into different sectors. Select correct option:Line graphSector graphsFrequency PolygonConversion Graphs49. The measurement of measure of degree of to which any two variables vary together is calledSelect correct option:Regression CoefficientCorrelationBoth (a) and (b)None of these50. Analysis of Variance (ANOVA) is a test for equality of:Select correct option:variancesmeansproportionsonly two parameters51. For some data you are given Maximum value = 96 , Minimum Value = 23 , Range = 73,number of classes selected between 5 and 15 Then class width will be Select correct option:1585All options 1,2 ,3 are possible52. If strength of the association between X and Y is very weak, then r = ? Select correct option:r = - 1r = 0r = 1r = 253. The moving averages of the Prices 90,70,30,110 are Select correct option:63.33, 7073.33, 8045.45, 6865.50, 7554. With increase in sample size, distribution tends to be a.......Select correct option:Meso kurticNormal

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Bell shapedAbove all55. In the central tendency Mean, Median and ModeSelect correct option:Mean is better than MedianMedian is better than ModeMean is better than ModeAll of these are true56. The degree to which numerical data tend to spread about an average is calledSelect correct option:The dispersionStandard deviationCorrelationNone of these57. …………..graphs are similar to bar graphs.Select correct option:columnlineconversionsector58. A pattern of variation of a time series that repeats every year is called:Select correct option:CyclicalSeasonalTrendSecular59. In the central tendency Mean, Median and ModeSelect correct option:Mean is better than MedianMedian is better than ModeMean is better than ModeAll of these are true60. The degree to which numerical data tend to spread about an average is calledSelect correct option:The dispersionStandard deviationCorrelationNone of these61. …………..graphs are similar to bar graphs.Select correct option:columnlineconversionsector62. A pattern of variation of a time series that repeats every year is called:Select correct option:CyclicalSeasonal

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TrendSecular63. You have measured the systolic blood pressure of a random sample of 22 employees of acompany. A 95% con?dence interval for the mean systolic blood pressure for the employees iscomputed to be (120,138). Which of the following statements gives a valid interpretation of thisinterval?Select correct option:About 95% of the sample of employees has a systoliAbout 95% of the employees in the company have aIf the sampling procedure were repeated many timesIf the sampling procedure were repeated many times64. Assume that a population consists of 7 similar containers having the following weights (km):9.8, 10.2, 10.4, 9.8, 10.0, 10.2, 9.6 What is the second moment about mean?Select correct option:0.262 kg0.069kg0.521 kg0.313kg65. How many numbers of parameter(s) are in t-distribution?Select correct option:01 pg 2922366. With increase in sample size, distribution tends to be a.......Select correct option:Meso kurticNormalBell shapedAbove all67. F-distribution is a…………….. distribution.Select correct option:Unimodel pg 312BimodalDiscreteNegatively skewed68. Which one of the following sampling methods would give unbiased results, if you need to findout the number of people in your town liking vanilla or chocolate ice creams?Select correct option:Ask my neighborsRandomly select a few ice cream shops in town, andAsk my friendsAsk my classmates

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69. A standard deviation obtained from sampling distribution of sample statistics is known asSelect correct option:Sampling ErrorStandard error pg 24070. If the regression line: Y= 3+5X meets y-axis at ‘8’ units distance from origin then the value ofx-intercept isSelect correct option:-(3/5)3/511/5171. Sum of three terms whose mean is equal to 90 isSelect correct option:27030Also 90None of these270/3=9072. FREQUENCY Function calculates how often values occur within a range of values.Select correct option:trueFalse73. Which of the following correlation coefficients represents the weakest correlation between twovariables?Select correct option:0.15-0.150.02-1.0074. If the value of r is 0.8 ,then the coefficient of determination isSelect correct option:67%64%80%75%75. If the dependent variable increases with the independent variable then the coefficient ofcorrelation isSelect correct option:0 to -10 to – 0.50 to -20 to 176. F- distribution tends to normality, if

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Select correct option:V1~8V2~8V1 and V2 ~8Sample size is large77. Consistency of an estimator can be checked by comparingSelect correct option:MeanMSEVarianceStandard deviation78. A standardized estimate has mean and varianceSelect correct option:(1, 0)(0, 1)(μ, s2)(μ, s)79. A composite hypothesis comprises of ………Select correct option:EqualityNot equal toLess than/greater(b) and (c)80. For a particular hypothesis test, a=0.05and B=0.05. The power of test is equal to:Select correct option:0.140.900.950.2581. In a t-distributionSelect correct option:Mean=median=modeMean>Median<ModeMedian >Mean>ModeMedia<Mode<Mean82. If we reject the null hypothesis, we might be makingSelect correct option:Type I errorType II errorA correct decisionUnpredictable83. The Central Limit Theorem is important in Statistics because it allows us to use the normaldistribution to make inferences concerning the population mean:Select correct option:Provided that the population is normally distributed aProvided that the population is normally distributed (Provided that the sample size is reasonably large (fo

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Provided that the population is normally distributed and the population variance is known (forany sample size)84. Herbicide A has been used for years in order to kill a particular type of weed, but anexperiment is tobe conducted in order to see whether a new herbicide, Herbicide B, is more effective thanHerbicide A.Herbicide A will continue to be used unless there is sufficient evidence that Herbicide B is moreeffective.The alternative hypothesis in this problem is thatSelect correct option:Herbicide A is more effective than Herbicide BHerbicide B is more effective than Herbicide AHerbicide A is not more effective than Herbicide BHerbicide B is not more effective than Herbicide A85. A data in which we study about Regions is called……Select correct option:QualitativeQuantitativeGeographicalChronological86. If the median of an arrangement of numbers is equal to the mean of its middle terms then thearrangement containsSelect correct option:Odd number of termsEven number of termsUnlimited number of termsPrime number87. If the graph is very much scattered, then what can be the suitable value of r?Select correct option:r = - 0.9r = -0.5r = 0.1r=0.888. In scatter diagram, clustering of points around a straight line indicatesSelect correct option:Linear regressionNon-linear regressionCurvilinear linear regressionBoth a and b89. If the standard deviation of a population is 9, the population variance isSelect correct option:39 21.3581

190

90. How many steps are involved in general procedure for testing hypothesis:4567 91. When testing for independence in acontingency table with 2rows and 5columns, there are________ degrees of freedom.41075 r-1*c-12-1*5-1=492. The critical region is in:The middle of a distributionThe tails of a distributionEither the middle or the tails of a distributionNeither the middle nor the tails of a distribution93. t-distribution is used to test the hypothesis about.....MeanproportionThe term 1-B is calledLevel of the testpower of the testSize of the testCritical region94. The asymptotic distribution of t-statistic with n-degree of freedom isFNormalZ T95. The Gallup Poll has decided to increase the size of its random sample of Canadian voters fromabout 1200 people to about 4000 people. The e?ect of this increase is to:Reduce the bias of the estimateIncrease the standard error of the estimateReduce the variability of the estimateIncrease the con?dence interval width for the parameter96. The value of chi square can never be :ZeroLess then 1Greater then 1Negative97. The curve of the F- distribution depends upon:MeanVarianceStandard DeviationSample Size98. We want to test H0 : μ = 1.5 vs. H1 : μ 6= 1.5 at _= .05 . A 95% confidence interval for μcalculated from a given random sample is (1.4, 3.6)Based on this finding we:Fail to reject H0

191

Reject H0Cannot make any decision at all because the value of the test statistic is not availableCannot make any decision at all because (1.4, 3.6) is only a 95%99. When we want to test the equality of two variances we usually useF-testChi-square testANOVAZ_test100. To find the estimate of a parameter…….methods are used.TwoThreeFourMany101. In testing hypothesis, we always begin it with assuming that:Null hypothesis is trueAlternative hypothesis is trueSample size is largePopulation is normal102. t-distribtion is applicable in case ofIndependent samplesDependent samplesBoth (a) and (b)Normal populations103. When testing for independence in a contingency table with 3 rows and 4 columns, there are________ degrees of freedom.567 12104. The Chi- Square distribution is continuous distribution ranging from:0 = ?2= 8-8 =?2 =0-8 =?2 =1-8 = ?2= 8105. The location of the critical region depends upon:Null hypothesisAlternative hypothesisValue of alphaValue of test-statistic106. A random sample of n = 6 has the elements 6, 10,13,14,18 and 20.What is the pointestimate of the population mean?1213.51111.5107. ML estimators may not ………ConsistentEfficientUnbiased

192

Bised108. Which of the following reveals the weakest fact.Select correct option:The measure of central tendency measures that value which depends only on the extreme valuesThe measure of central tendency measures that value in tha data which occurs in the data most frequenttimes.The measure of central tendency measures the value which has tendency to lie in the central part of thedata.109. The measure of central tendency measures the distance of values from meansFrequency polygon is …………Select correct option:Bar ChartsA line graphPareto ChatsNone of these110. A bar graph uses ……to show data.Select correct option:PointsBarsLinesPictures111. Geographical data deals with…Select correct option:ReligionHeightIncomeRegions112. Which one provides the basis for hypothesis testing?Null hypothesisAlternative hypothesisCritical valueTest-statistics113. The test statistic to test the U1 = U2 (U represent the mean of population)for normalpopulation for n>30.F-testZ-testT-testChi-Square test114. In a t-distributionMean=median=modeMean>Median<ModeMedian >Mean>ModeMedia<Mode<Mean115. 1-a is the probability of ......

193

Type 1 errorRejection regionAcceptance regionType 2 error116. Inferential statistics involves …….TestingConfidence intervalEstimationAbove all117. Probability of type II error isaB 1-a1-B118. if the equation of regression line is y = 5, then what result will you take out from it?Select correct option:The line passes through origin.The line passes through (5, 0)The line is parallel to y-axis.The line is parallel to x-axis.119. If the estimating equation is Y = a – b X ,Which of the following is trueSelect correct option:a)The y intercept is’b’b) Slope of line is negativec) There is inverse relationshipd) b & c120. The variance of t-distribution, for v >2, is always:Select correct option:Greater than zeroLess than oneEqual to oneGreater than one121. Alpha is the probability of ......Select correct option:Rejecting H0Accepting H0Rejecting H1Accepting H1122. What type of data is collected in population census?Select correct option:Two Types123. The collection of all outcomes for an experiment is calledSelect correct option:a sample spacethe intersection of eventsjoint probabilitypopulation124. Which of the graph is used for a time series data:

194

Select correct option:Frequency curveFrequency polygonHistorigramHistogram125. A histogram is consists of a set of adjacent rectangles whose bases are marked off by:Select correct option:Class boundariesClass limitsClass frequencyClass marks126. The value that has half of the observations above it and half the observations below it isknown as:Select correct option:MeanMedianModeStandard deviation127. The height of a student is 60 inches. This is an example of ...........?Select correct option:Continuous dataQualitative dataCategorical dataDiscrete data128. Range of the values -2,-3,-4,-3,-9,-2,-8,-1,0 isSelect correct option:0-9890-9=-9129. If the both tails of the distribution are equal, then distribution is called:Select correct option:J-shapedSymmetricalPositively SkewedNegatively Skewed130. Ranking scale also include the properties of which scale?Select correct option:Nominal scaleInterval scaleRatio scaleAll of these131. Range of the values -2.50,-3.70,-4.80,-3.10,-9.70,-2.20,-8.90,-1.60, 0.60 isSelect correct option:10.0310.30

195

9.109.000.60+9.70=10.30132. What is/are the mode for the following data: 1,m,d,n,,2,d,2,d,s,5,5,7Select correct option:2d5 2,d,5133. If the standard deviation of a population is 5.5, the population variance is:Select correct option:5.5312530.25134. What we commonly called a bell shaped distribution:Select correct option:symebi moderu shapskewed135. The beginnings of a cumulative frequency distribution are presented below. What is thenext number in the Cumulative Frequency column? Classes Frequency Cumulative Frequency6.1 to 8 1 1 8.1 to 10 2 10.1 to 12 3Select correct option:0123136. Range of the values -10,- 19, -9, -15, -28, -26, -25 is:Select correct option:+18-18-19+19137. Which one of the following is less than median for a symmetrical distribution:Select correct option:50percentile51 percentile2quartile4decile138. The value of the middle term in a ranked (ordered) data set is called theSelect correct option:modemeanmedianharmonic mean139. Sum of absolute deviations of the values is least when deviations are taken fromSelect correct option:mean

196

medianmodeg.m140. Statistic is a numerical quantity, which is calculated fromSelect correct option:dataobservationsamplepopulation141. The branch of Statistics that is concerned with the procedures and methodology forobtaining valid conclusions is called:Select correct option:descriptiveadvanceinfernetialsample142. How to find the class midpoint?Select correct option:Half the sum of upper class limit and lower class limitFind the difference between consecutive lower limitsCount the number of observations in the classDivide the class frequency by the number of observ143. For given data, discuss the shape of the distribution: X f 0.2 8 1.2 15 2.2 23 3.2 40Select correct option:Positively skewedNegatively skewedSymmetric curveU- Shaped curve144. Data classified by attributes are called:Select correct option:groupqulitativequantitivearrayif ‘2’ is a leading digit in 24335, than what are the trailing digits in the observation todisplay a ‘Stem-and –Leaf display’.Select correct option:4 335433543145. A frequency polygon is obtained by plotting the class frequencies against what?Select correct option:classboundaycumulative frequencyrelative frequencymid point146. When more values are lying at the start of the distribution, it is:

197

Select correct option:u shapepositivenegativesymmetrica147. The data for an ogive is found in which distribution:Select correct option:A cumulative frequency distributionA joint frequency distributionA frequency distributionA relative frequency distribution148. Which one of the following is greater than median for a symmetrical distribution:Select correct option:1st Decile7th Decile44th Percentile14th Percentile149. Statistics deals withSelect correct option:IndividualsIsolated itemsIsolated itemsAggregates of facts150. Data classified by attributes are called:Select correct option:Grouped dataQualitative dataQuantitative dataArrayed data151. As a general rule, statisticians tends to use which of the following number of classes whenarranging the dataSelect correct option:Fewer than 5Between 5 & 20Between 8 & 15More than 20152. The collection of all outcomes for an experiment is calledSelect correct option:a sample spacethe intersection of eventsjoint probabilitypopulation153. If P (E) is the probability that an event will occur, which of the following must be false:Select correct option:P(E)= - 1

198

P(E)=1P(E)=1/2P(E)=1/3154. If we roll a die then probability of getting a ‘2’ will beSelect correct option:2/61/64/61155. In a multiplication theorem P (A n B) equals:Select correct option:P (A) P (B)P (A) + P (B)P (A) * P (B|A) pg 158P(B\A)*P(B)156. If Y=3X+5,then S.D of Y is equal toSelect correct option:9 s.d(x)3 s.d(x)s.d(x)+53s.d(x)+5157. In regression line Y=a+bX, X is called:Select correct option:Dependent variableIndependent variableExplained variableRegressand158. Symbolically, a marginal probability is:Select correct option:P(AB)P(AUB)P(A/B)P(A)159. Which formula represents the probability of the complement of event A:Select correct option:1 + P (A)1 - P (A)P (A)P (A) -1160. If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then P(A|B) = :Select correct option:0.650.050.030.07 not sure161. The probability of drawing a ‘white’ ball from a bag containing 4 red, 8 black and 3 white

199

balls is:Select correct option:0 3/151/121/2Total ball= 4+8+3=15P=3/15162. An expected value of a random variable is equal to:Select correct option:VarianceMeanStandard deviationQuartile163. When we toss a fair coin 4 times, the sample space consists of….points.Select correct option:48 1216164. 5C5=Select correct option:51 1025165. In a probability distribution, the sum of the probabilities is equal to:Select correct option:0 0.10.51166. The simultaneous occurrence of two events is called:Select correct option:Joint probabilitySubjective probabilityPrior probabilityConditional probability167. Let E and F be events associated with the same experiment. Suppose the E and F areindependent and that P(E) = 1/4 and P(F) = 1/2 Then P(E U F) is:Select correct option:1/83/47/85/8¼+1/2=3/4

Assignment No.3 (Course STA301)Fall 2010 (Total Marks 30)Muhammad Imran IlyasContact 0312469223103124692262

200

Assignment No. 3Question 1 2+2+6=10Marksa) Define Bernoulli trail and Binomial Experiment.Sol.Bernoulli TrailA sequence of Bernoulli trials occurs when a Bernoulli experiment isperformed several independent times so that the probability of success, say, p,remains the same from trial to trial. That is, in such a sequence we let p denote theprobability of success on each trial. In addition, frequentlyq = 1− p denote the probability of failure; that is, we shall use q and pBinomial ExperimentA binomial experiment (also known as a Bernoulli trial) is a statisticalexperiment that has the following properties:The experiment consists of n repeated trials.Each trial can result in just two possible outcomes. We call one of these outcomesa success and the other, a failure.The probability of success, denoted by p, is the same on every trial.The trials are independent; that is, the outcome on trial does not affect theoutcome on other trials.b) In which condition, Poisson distribution is used to approximate hyper geometricdistribution?Sol.Poisson distribution is not used to approximate hypergeometricdistribution but hypergeometric can be used to approximate poision than N is verylarge and successive terms K is very smallc) Find the probability that (i) No defective bolt (ii) at most 5 defective bolts will befound in a box of 200 bolts if it is known that 2 percent of such bolts are expectedto be defective.Sol.n = 200 , probability of defective bolts are 2% or p = .02μ = np = 200 * .02 = 4in poision Distribution is P (X = x ) =4!e μx

x-(i) No defective bolt(ii) At most 5 defective boltsP(x < = 5) = p(x = 0) + p(x = 1) + p(x = 2) + p(x = 3) + p(x = 4) + p(x = 5)= 0.0183 + 0.0732 + 0.1464 + 0.1952 + 0.1952 + 0.1562= 0.7428Question 2 3+5+2=10Marksa) If its rain, an umbrella salesman can earn $ 30 per day. If it is fair, he can lose $ 6 perday. What is his expectation if the probability of rain is 0.3?X P(x) X.P(x)30 0.3 9

201

-6 .7 -4.2Total 4.8E(X) = Σ X . P(x) = 4.8b) Show that the following is a density function.f(x) =2x0 < x < 2= 0 elsewheref(x) =2xf(0) = 0/2 = 0f(2) = 2/2 =1we know that function is a density function if total probability is 1p( 0 < x < 2 ) = 1L.H.S. = p( 0 < x < 2 )= [f(2) + f(0)] * 2 / (2 – 0)= [(1) + (0)] *2 / 2= 1 so it is density functionc)( )( )0,1 3/ 28 (0) 5 / 281/ 0If we have f and fthen find f= =Sol.f (1/0) = f( 0 , 1 ) / f( 0 )= (3/28) / (5/28)= 3 / 5Question 3 2+2+6=10Marksa) From the following table find P(X + Y < 1);Sol.P(X + Y < 1) = f( 0,0) + f( 0,1) + f( 1,0)= 3/28 + 6/28 + 9/28= 18/28= 9/14b) Write this expression h (3; 70, 20, 5) in probability notations/function.c) An electrical firm manufactures light bulbs that have a length of life that is normallydistributed with mean equal to 800 hours and a standard deviation of 40 hours. Find theprobability thatJoint Probability YX0 3/

202

(i) A bulb will burn between 778 and 834 hours.(ii) A bulb will burn in less than 778 hours.Sol.μ = 800 , σ = 40(i) A bulb will burn between 778 and 834 hours.Z1 = (X1 - μ)/ σ= (778 – 800) / 40= -22 / 40= -0.55Area between μ and 778 at z = -.55 is 0.2088Z2 = (X2 - μ)/ σ= (834 – 800) / 40= 34 / 40= 0.85Area between μ and 834 at z = 0.85 is 0.3023SoArea between 778 and 834 = 0.3023 + 0.2088= 0.5111(ii) A bulb will burn in less than 778 hours.Z = (X - μ)/ σ= (778 – 800) / 40= -22 / 40= -0.55Area between μ and 778 at z = -.55 is 0.2088SoThe Area less than 778 = 0.5 – 0.2088= 0.2912Question No: 1 ( Marks: 1 ) - Please choose one



► Equally likely


► Exhaustive



203

►

►

►

►



► Rejected

► Accepted

► No conclusion

► Acknowledged



204

► Variances

► Means

► Proportions

► Groups



► Helmert

► Pearson

► R.A Fisher

► Francis



► Z-test PROPORTIONS ARE TESTED AND MEAN

► t-Test MEAN IS TESTED

► Both Z & T-test

► F test VARIANCE AND STANDARD DEVIATION



205

► 0,1,2,3

► 1,3,3,1

► 1, 2, 3

► 3, 2


If X and Y are independent variables, then E (XY) is:

► E(XX)

► E(X).E(Y)

► X.E(Y)

► Y.E(X)



► x & n

► x & p

► n & p

► x, n & p


206


► P(E)= - 1 ROBIBILITY SHOULD NEVER BE NEGATIVE AND NOT BE GREATER THAN ONE

► P(E)=1

► P(E)=1/2

► P(E)=1/3



► E (T) =

EXPECTION OF STATISTIC IS EQUAL TO PARAMETER THAT IS ESTIMATED THEN STATISTIC IS CALLED UNBIASED OTHER WISE BIASED.

► E (T) =T

► E (T) =0

► E (T) =1



207

► Sample mean

► Sample median


► Sample variance





IF IT IS DI VIDED BY N-1 THEN IT IS CALLED UNBIASED OTHER WISE BIASED


► None of these


208


1

0

c

-c

► 0

► 1

► c THE EXPECTION OF A CONSTATNT IS ALWAYS CONSTANT

► -c



is:

►

209

►

►

►


The analysis of variance technique is a method for :











210



► Equal to 100


► Less than 100



The branch of Statistics that is concerned with the procedures and methodology for obtaining valid conclusions is called:







► Classification

► Tabulation

211

► Bar chart




►

►

►

►


In normal distribution

► 1

► 2

► 3

► 0

212



► Ogive


► Frequency curve

► Historigram








When ,what is the value of Median, if the distribution is

symmetrical:

► 1

► 2

► 3

► 4

213









► 5

► 8

► 9 n-1

► 10




It is shown by h0 and first we assumption is h0




214



► Type I error

► Type II error




How to find ?

► f(0, 0) + f(0, 1) + f(1, 2)

► f(2, 0) + f(0, 1) + f(1, 0)

► f(0, 0) + f(1, 1) + f(1, 0)

► f(0, 0) + f(0, 1) + f(1, 0)


How many parameters are involved in hypergeometric distribution?

215

Three N n k

Poission mean is np and variance and mean are equal


If an automobile is driven on the average no more than 16000 Km per year, then formulate the null and alternative hypothesis.


Write down the test statistic when chi- square goodness of fit test is performed.


Find the value of F(table value), when 1n 7 , 2n 10 and α= 0.05

3.37


216

If X = 327, n = 634, 0.50 then find the z-test statistic for proportion.


If population proportions are given as:

Find ,where n = 10

= p1q1/n1+p2q2/n2


A candidate for mayor in a large city hires the services of a poll-taking organization, and they found that 62 of 100 educated voters interviewed support the candidate, and 69 of 150 uneducated voters support him.

At the 0.05 significance level, test the following

Book Example # 16.17 on Page 155

Professor sher Muhammad Chaudhry

217


If we have RCBD with MSE=3.19, no.of.treatments = 4, no.of.blocks = 5; then find the value of LSD (least significant difference) for treatments by using α=0.05 and error degrees of freedom is 12.


Find the mean and variance for the sampling distribution given below.

p̂ No. of Samples

Probability p̂f

0 1 1/20 1/3 9 9/20 2/3 9 9/20 1 1 1/20

20 1

F( ) F( ) F( )

0 1/20

1/3 9/20

2/3 9/20

1 1/20

1

218

Mean=

Variance=

In a multiplication theorem P (A and B) equals:


P (A) P (B)

P (A) + P (B)

P (A) * P (B|A)

P(B\A)*P(B)

The probability can never be:


1

1/2

1

219

-1/2

If two fair die are thrown, the probability of getting a double six is:


1/6

2/36

1/36

1/12

If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then P(A|B) = :


0.65

0.05

0.03

0.07

Twenty percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomial distribution is:


20

2

220

4

16

If f(x) is a continuous probability function, then P(X = 2) is:


1

0

1/2

2



Less than one

Greater than one


Zero

Question # 8 of 10 ( Start time: 01:38:25 PM )

Total Marks: 1

E(4X + 5) =__________


12 E (X)

221

4 E (X) + 5

16 E (X) + 5

16 E (X)

The location and shape of the normal curve is (are) determined by:


Mean

Variance

Mean & variance

Mean & standard deviation

The probability of success changes from trial to trial, is the property of:


Binomial experiment

Hypergeometric experiment

Both binomial & hypergeometric experiment

Poisson experiment

MIDTERM FALL [email protected] 08-12-2010 (1st session)STA301Question No: 1 (Marks: 1) - Please choose oneIf a player well shuffles the pack of 52 playing cards, then the probability of a black cardfrom 52 playing cards is:

222

152►1352►452►2652►Question No: 2 (Marks: 1) - Please choose oneThe probability of drawing a ‘jack card ‘from 52 playing cards is:► 152452►1352►2652►Question No: 3 (Marks: 1) - Please choose oneIn a regression line Y= a + bX, the value of the correlation coefficient will be zero if:► Intercept a = 0► Intercept a ≠ 0► Slope b = 0► Slope b ≠ 0Question No: 4 (Marks: 1) - Please choose oneWhich one of the following measurement does not divide a set of observations into equalparts?► Quartiles► Deciles► Percentiles► Standard deviationsQuestion No: 5 (Marks: 1) - Please choose oneWhich one of the following graphs is used for a time series data?► Histogram► Historigram► Frequency curve► Frequency polygonQuestion No: 6 (Marks: 1) - Please choose oneIf you connect the mid-points of rectangles in a histogram by a series of lines that alsotouches the x-axis from both ends, what will you get?► Ogive

223

► Frequency polygon► Frequency curve► HistorigramQuestion No:7 (Marks: 1) - Please choose oneWhich one is equal to explained variation divided by total variation?• Sum of square due to regression• Coefficient of determinant• Standard error estimate• Coefficient of correlation (not confirmed)Question No: 8 (Marks: 1) - Please choose onein the given series 1,2,1,1,2,2,2,3,4,5,3,2,3,1,4,2,3 mode of given is• 43• 312•3211• 3 (not confirmed)2*

Question No: 9 (Marks: 1) - Please choose oneTrue for the population,• it must be large number of values• It must refer to people• It is collection of individual objects or measurement not confirmed)• It is the small part of wholeQuestion No:10 (Marks: 1) - Please choose oneData arrangement in ascending or descending order• Array data• Group data• Ungroup data• Raw dataQuestion No: 11 (Marks: 1) - Please choose oneWhat is the main objective of Descriptive statistics?• To test population properties• To describe the data we collected• To infer something about the population• Making estimateQuestion No: 12 (Marks: 1) - Please choose oneWhich measure of central tendency?• Variation of distribution• Average of distribution• Scattering of distribution• Dispersion of distribution

224

Question No: 13 (Marks: 1) - Please choose oneIf a=4 b=2 estimate line (i.e y=a+bx) and independent veriable has value 3 the the valueof dependent veriable• 6• 9• 10• 11Question No: 14 (Marks: 1) - Please choose oneThe number of ways in which 4 books can be arranged• 4• 6• 12• 24Question No: 15 (Marks: 1) - Please choose oneIf we plot paired observed (x,y)=1…….n on graph is called,• Polygon• Freasito diagram• Scatter diagram• Cumulative frequency diagramQuestion No: 16 (Marks: 1) - Please choose oneThe simultaneous occurrence of two events is called• Descriptive probability• Subjective probability not confirmed• Conditional probability• Joint probabilityQuestion No: 17 (Marks: 1) - Please choose oneWhich one is the not measure of dispersion.• The range• 50th percentile• Inter quartile range• Variance not confirmedQuestion No: 18 (Marks: 1) - Please choose oneIn positively skew cure which relation is• The mean, median and mode are equal• Mean is greater then median not confirmed• Median is greater then mean• Standard deviation must be greater then mean or medianQuestion No: 19 (Marks: 1) - Please choose oneWhen coin tossed we get only1 outcome2 outcomes3 outcomes4 outcomesQuestion No: 20 (Marks: 1) - Please choose oneWhen mean is 25 and S.D is 5 then CV is• 100%

225

• 25%• 20% not confirmed• 10%Question No: 21 (Marks: 2) - Please choose oneDefine rule for permutationQuestion No: 22 (Marks: 2) - Please choose oneIf mean x=0.645 and S2 =0.215Then calculate coefficient of variationQuestion No: 23 (Marks: 3) - Please choose oneFind the probability of drawing white ball from bag out of 4 red, 8 blue and 3 whiteballs.Question No: 24 (Marks: 3) - Please choose oneIf the equation of the least square regression line arey=2.64+0.648 andX=-1.91+0.917xFind coefficient of r.Question No: 25 (Marks: 5) - Please choose oneA and B are two independent events, ifP(A)=0.40, P(B)=0.30Find Probabilities i) P (A∩B)ii) P(A’∩B’Question No: 26 (Marks: 5) - Please choose oneIf S={1,2,3,4,5,6,7,8,9,10}AndA={1,2,3,4} , B= {3,4,5,6}Prove that(A ∪ B) = (A ∩ B)

MIDTERM EXAMINATION (Spring 2010)

STA301- Statistics and Probability (Session - 4)

Time: 60 min Ref No: 1514379 Marks: 40

Student Info

Student ID: MC090407150

Center: OPKST

Exam Date: 5/30/2010 12:00:00 AM

For Teacher's Use Only

Q No. 1 2 3 4 5 6 7 8 Total

226

Marks

Q No. 9 10 11 12 13 14 15 16

Marks

Q No. 17 18 19 20 21 22 23 24

Marks

Q No. 25 26

Marks

Question No: 1 (Marks: 1) - Please choose one

10! =………….

► 362880

► 3628800

► 362280

► 362800


If a player well shuffles the pack of 52 playing cards, then the probability of a black card from 52 playing cards is:

►

►

►

227

►


The probability of drawing a ‘jack card ‘from 52 playing cards is:

►

►

►

►


Which dispersion is used to compare variation of two series?

► C.V.

► Q.D.

► M.D.

► S.D.


If all the values fall on the same straight line and the line has a positive slope then what will be the value of the correlation coefficient ‘r’:

228

► 0 ≤ r ≤ 1

► r ≥ 0

► r = +1

► r=-1


I

n a regression line Y= a + bX, the value of the correlation coefficient will be zero if:

► Intercept a = 0

► Intercept a ≠ 0

► Slope b = 0

► Slope b ≠ 0


When two coins are tossed the probability of at least one head is:

► 1/4

► 3/4

► 2/4

► 4/4


Which one of the following measurement does not divide a set of observations into equal parts?

229

► Quartiles

► Deciles

► Percentiles

► Standard deviations


In the model Y = mX + a, Y is also known as the:

► Predictor variable

► Independent variable

► Predicted (dependent) variable

► Explanatory variable


According to empirical rule approximately 95% of the measurements will fall under which interval?

► X S

► 2X S

► 3X S

► 4X S

230


Which one of the following is written at the top of the table?

► Source note

► Foot note

► Prefatory note

► Title


If a curve has a longer tail to the right, it is called:



► J-shaped

► Symmetric


Which one of the following is the class frequency?





231


If X is a discrete random variable, then the function is

► A probability function

► A probability density function

► A density function

► A distribution function


Which one of the following graphs is used for a time series data?

► Histogram

► Historigram

► Frequency curve




► Ogive


► Frequency curve

► Historigram

232


If mean of the two observations is 10.5, then median of these two observations will be:

► 7.5

► 8.5

► 9.5

► 10.5


Which one is the formula of mid range?

►

►

►

►


Which one of the following is not included in measures of central tendency?

► Quartile deviation

► Harmonic mean

► Geometric mean

► Arithmetic mean

233


For the given data 2, 3, 7, 0, -8 G. M will be:

► Negative

► Positive

► Zero

► Undefined

Question No: 21 (Marks: 2)

Why measure of central tendency and measure of dispersion are complementary to each other?

Answer: Together both measures give us adequate description of data.


What do you know about discrete random variable?

Answer:

Such a numerical quantity whose value is determined by the value of a random experiment is called a random variable.

Example: If we toss three dice together and let X represents the number of heads, then the random variable X consists of the value 0, 1, 2, and 3. the X in this example is a discrete random variable.

234


What is the subjective approach to the probability?

Answer:

Subjective probability is a measure of the strength of a person’s belief regarding the occurrence of an event A. Probability in this sense is purely subjective and is based on whatever evidence is available to the individual.

It has a disadvantage that two or more persons faced with the same evidence may arrive at different probabilities.

Example:

Suppose a panel of three judges is hearing a trial. It is possible that based on the evidence that is presented; two of them arrive at the conclusion that the accused is guilty while one of them decides that the evidence is not strong to draw this conclusion.


Explain the difference between absolute dispersion and relative dispersion:

Answer:


Differentiate between the mutually exclusive events and exhaustive events.

Answer:

235

Mutually Exclusive Events: Two events A and B of a single experiment are said to be mutually exclusive if and only if they both can’t occur at the same time.

Example:

When a die is rolled, the events ‘even number’ and odd number are mutually exclusive as we can get either an even number or an odd number in one throw, not both at the same time.

Exhaustive Events: Events are said to be collectively exhaustive, when the union of mutually exclusive events is equal to the entire sample space S.

Examples:

In the coin tossing experiment, head and tail are collectively exhaustive events.


Find the first two moments about mean from the following data.

X= 34, 70, 42, 54, 40, 68, 56, 38, 36, 72


1- Hypothesis refers to

2. The outcome of an experiment

3. A conclusion drawn from an experiment

4. A form of bias in which the subject tries to outguess the experimenter

5. A tentative statement about the relationship

2- Statistics is used by researchers to

236

2.Analyze the empirical data collected in a study

3.Make their findings sound better

4.Operationally define their variables

5.Ensure the study comes out the way it was intended

3- A literature review requires

(6)Planning

(7)Good & clear writing

(8)Lot of rewriting

(9)All of the above

4- A literature review is based on the assumption that

Copy from the work of others

Knowledge accumulates and learns from the work of others

Knowledge disaccumulates

None of the above option

5- A theoretical framework

ii) Elaborates the r/s among the variables

iii) Explains the logic underlying these r/s

iv) Describes the nature and direction of the r/s

v) All of the above

6- Which of the following statement is not true?

A research proposal is a document that presents a plan for a project

A research proposal shows that the researcher is capable of successfully conducting the proposed research project

A research proposal is an unorganized and unplanned project

A research proposal is just like a research report and written before the research project

237

7- Preliminary data collection is a part of the


3. Descriptive research

4. Exploratory research

5. Applied research

6. Explanatory research

8- Conducting surveys is the most common method of generating

iv. Primary data

i. Secondary data

v. Qualitative data

vi. None of the above

9- After identifying the important variables and establishing the logical reasoning in theoretical framework, the next step in the research process is

iv. To conduct surveys

v. To generate the hypothesis

vi. To focus group discussions

vii. To use experiments in an investigation

10- The appropriate analytical technique is determined by

(d) The research design

(e) Nature of the data collected

(f) Nature of the hypothesis

(g) Both A & B

11- Personal interviews conducted in shopping malls are known as:

a. Mall interviewsb. Mall intercept interviewsc. Brief interviewsd. None of the given options

238

12-WATS lines provided by long distance telephone service at fixed rates. In this regard, WATS is the abbreviation of:

e. West Africa Theological Seminaryf. Washtenaw Area Transportation Studyg. Wide Area Telecommunications Serviceh. World Air Transport Statistics

13-A list of questions which is handed over to the respondent, who reads the questions and records the answers himself is known as the:

i. Interview schedulej. Questionnairek. Interview guidel. All of the given options

14-One of the most critical stages in the survey research process is:

m. Research designn. Questionnaire designo. Interview designp. Survey design


15-Question that consists of two or more questions joined together is called a:

q. Double barreled questionr. General questions. Accurate questiont. Confusing question

16-The number of questionnaires returned or completed divided by the total number of eligible people who were contacted or asked to participate in the survey is called the:

u. Response ratev. Participation ratew. Inflation ratex. None of the given options

17-To obtain the freest opinion of the respondent, when we ask general question before a specific question then this procedure is called as the:

239

y. Research techniquez. Qualitative techniqueaa. Funnel techniquebb. Quantitative technique

18-A small scale trial run of a particular component is known as:

cc. Pilot testingdd. Pre-testingee. Lab experimentsff. Both A & B

18-Field testing of the questionnaire shows that:

gg. Respondents are willing to co-operatehh. Respondents are not willing to co-operateii. Respondents do not like any participationjj. All of the given options


kk. Self-administered questionnairesll. Office assistantmm. Managernn. None of the given options


oo. Self-administered questionnairespp. Office assistantqq. Managerrr. None of the given options

21-Discrete variable is also called……….

I. Categorical variable J. Discontinuous variableK. Both A & B L. None of the above

22-“Officers in my organization have higher than average level of commitment” Such a hypothesis is an example of……….

1. Descriptive Hypothesis2. Directional Hypothesis3. Relational Hypothesis4. All of the above

240

23-‘Science’ refers to……….

1. A system for producing knowledge 2. The knowledge produced by a system3. Both A & B4. None of the above

24-Which one of the following is not a characteristic of scientific method?

DeterministicResearch Method (STA 630) Success Objectives

Rationalism Empirical Abstraction

25-The theoretical framework discusses the interrelationships among the……….

Variables Hypothesis Concept Theory

26-………research is based on naturalism.

Field research Descriptive research Basic research Applied research

27-Personal interviews conducted in shopping malls are known as………

Mall interviews Mall intercept interviews Brief interviews None of the given options

28- ……… is used to obtain the freest opinion of the respondent, by asking general question before a specific question.

Research technique Qualitative technique Funnel technique

241

Quantitative technique

29-In, ___________the interviewer and members jointly control the pace and direction of the interview.

Field interview Telephonic interview Both A and B None of the given options

30-Randomization of test units is a part of ………

Pretest Posttest Matching Experiment

31- Rationalism is the application of which of the following?



C. Reasoning


32- On which of the following, scientific knowledge mostly relies?



C. Prior knowledge


33- Which of the following refers to research supported by measurable

evidence?

A. Opinion

B. Empiricism

C. Speculation

242

D. Rationalism

34-Research method is applicable in all of the following fields, EXCEPT;

A. Health care

B. Religion


C. Business


35- All of the following are true statements about action research, EXCEPT;



C. Results are generalizable


36-Which of the following is characteristic of action research?




D. Results demonstrate cause-and-effect relationships

37-If a researcher is studying the effect of using laptops in his classroom to ascertain their merit and worth; he is likely conducting which of the following types of research?

A. Experimental

B. Applied

C. Basic

243

D. Evaluation

38- Exploratory research addresses which of the following types of question?

A. If

B. How

C. Why

D. What

39- Which of the following is not the source for getting information for exploratory research?

A. Content analysis

B. Survey

C. Case study

D. Pilot study

40- Which of the following is the main quality of a good theory?





41- A variable that is presumed to cause a change in another variable is known as:





42- Which of the following is the opposite of a variable?244

A. An extraneous variable


C. A data set

D. A constant

43- Which of the following is not a concept?

A. Leadership




44- Which of the following can best be described as a categorical variable?

A. Age

B. Annual income


D. Religion


45-“Income distribution of employees” in a specific organization is an example of which of following type of variable?





245

46-“There is no relationship between higher motivation level and higher efficiency” is an example of which type of hypothesis?

A. Alternative

B. Null

C. Co relational

D. Research

47- Which of the following is not a role of hypothesis?





48-Hypothesis test may also be called as:

A. Informal test

B. Significance test

C. Moderating test

D. T-test

49-Which type of review compares how different theories address an issue?

A. Context review




50-After you locate a source, you should write down all details of the reference, EXCEPT;

A. Volumes

246

B. Titles

C. Price


51- ___________research is based on naturalism.

A. Field research

B. Descriptive research

C. Basic research

D. Applied research

52- Personal interviews conducted in shopping malls are known as_________

A. Mall interviews

B. Mall intercepts interviews

C. Brief interviews


53- ____________is used to obtain the freest opinion of the respondent, by asking

general question before a specific question.

A. Research technique

B. Qualitative technique

C. Funnel technique

D. Quantitative technique

54- In, ____________the interviewer and members jointly control the pace and

direction of the interview.

A. Field interview

247

B. Telephonic interview

C. Both A and B



55- Randomization of test units is a part of ______________

A. Pretest

B. Posttest

C. Matching

D. Experiment

56- Which one of the following sets is the measure of central tendency?

a. Mean, standard deviation, mode

b. Mean, median, standard deviation

c. Arithmetic mean, median, mode

d. Standard deviation, internal validity, mode

57- Internal validity refers to.

a. Researcher’s degree of confidence.

b. Generalisability

c. Operationalization

d. All of the above

58- How many times the students appear in the research class is the example of _________.

a. Intensity

248

b. Space

c. Frequency

d. Direction

59- Time consumed in mall intercept interview is .

a. High

b. Moderate

c. Low

d. Nil

60- Departmental stores selected to test a new merchandising display system is

the example of .

a. Quota sampling

b. Convenience sampling

c. Judgmental sampling

d. Purposive sampling

61- In ___________, the researcher attempts to control and/ or manipulate the variables in

the study.

1. Experiment

2. Hypothesis


4. Research design

62- In an experimental research study, the primary goal is to isolate and identify the effect

249

produced by the ____.





63- A measure is reliable if it provides consistent ___________.

1. Hypothesis

2. Results

3. Procedure

4. Sensitivity

64- The interview in which questions are already prepared is called ________.






65-The numerical description that describe sample may be expected to differ from those

that describe population because of random fluctuations inherent in sampling process.

1. Sampling design


3. Sampling error

250


66- In ______________ , each population element has a known and equal chance of

selection.


2. Quota sampling



67- ______ is the evidence that the instrument, techniques, or process used to measure

concept does indeed measure the intended concepts.

1. Reliability

2. Replicability

3. Scaling

4. Validity

68- A researcher is interested in studying why the “new math” of the 1960s failed. She interviews several teachers who used the new math during the 1960s. These teachers are considered as:

1. Primary sources


3. External critics

4. Internal critics

69- Which of the following is NOT true about stratified random sampling?



251

proportions




70- Experimental design is the only appropriate design where_________ relationship can

be established.

1. Strong

2. Linear

3. Weak

4. Cause and Effect

71. Discrete variable is also called……….

M. Categorical variable N. Discontinuous variableO. Both A & B P. None of the above

72.“Officers in my organization have higher than average level of commitment”


5. Descriptive Hypothesis6. Directional Hypothesis7. Relational Hypothesis8. All of the above

73.‘Science’ refers to……….

5. A system for producing knowledge Research Method (STA 630) Success Objectives

6. The knowledge produced by a system7. Both A & B8. None of the above

252

74.Which one of the following is not a characteristic of scientific method?

Deterministic Rationalism Empirical Abstraction

73.The theoretical framework discusses the interrelationships among the……….

Variables Hypothesis Concept Theory

74.………research is based on naturalism.

Field research Descriptive research Basic research Applied research

75.Personal interviews conducted in shopping malls are known as………

Mall interviews Mall intercept interviews Brief interviews None of the given options

76.……… is used to obtain the freest opinion of the respondent, by asking general question before a specific question.

Research technique Qualitative technique Funnel technique Quantitative technique

77.In, ……… the interviewer and members jointly control the pace and direction of the interview.

Field interview Telephonic interview Both A and B None of the given options

253

78.Randomization of test units is a part of ………

Pretest Posttest Matching Experiment

79. In ___________, the researcher attempts to control and/ or manipulate the variables in the study.

1. Experiment

2. Hypothesis


4. Research design

80. In an experimental research study, the primary goal is to isolate and identify the effect produced by the ____.





81. A measure is reliable if it provides consistent ___________.


1. Hypothesis

2. Results

3. Procedure

4. Sensitivity

254

82. The interview in which questions are already prepared is called ________.





83. The numerical description that describe sample may be expected to differ from those that describe population because of random fluctuations inherent in sampling process.

1. Sampling design


3. Sampling error


84. In ______________ , each population element has a known and equal chance of

selection.


2. Quota sampling



85. ______ is the evidence that the instrument, techniques, or process used to measure concept does indeed measure the intended concepts.

1. Reliability

2. Replicability

3. Scaling

4. Validity

255

86. A researcher is interested in studying why the “new math” of the 1960s failed. She interviews several teachers who used the new math during the 1960s. These teachers are considered as:

1. Primary sources


3. External critics

4. Internal critics

87. Which of the following is NOT true about stratified random sampling?



proportions




88. Experimental design is the only appropriate design where_________ relationship can be established.

1. Strong

2. Linear

3. Weak

4. Cause and Effect

89. Rationalism is the application of which of the following?



C. Reasoning

256


90. On which of the following, scientific knowledge mostly relies?




C. Prior knowledge


91. Which of the following refers to research supported by measurable

evidence?

A. Opinion

B. Empiricism

C. Speculation

D. Rationalism

92. Research method is applicable in all of the following fields, EXCEPT;

A. Health care

B. Religion

C. Business


93. All of the following are true statements about action research, EXCEPT;



C. Results are generalizable257


94. Which of the following is characteristic of action research?




D. Results demonstrate cause-and-effect relationship

95. If a researcher is studying the effect of using laptops in his classroom to

ascertain their merit and worth, he is likely conducting which of the

following types of research?

A. Experimental

B. Applied

C. Basic

D. Evaluation

96. Exploratory research addresses which of the following types of

question?

A. If

B. How

C. Why

D. What

97. Which of the following is not the source for getting information for

exploratory research?

A. Content analysis

258

B. Survey

C. Case study

D. Pilot study

98. Which of the following is the main quality of a good theory?





100. Which of the following is not a concept?

A. Leadership




101. A variable that is presumed to cause a change in another variable is

known as:






102. Which of the following is the opposite of a variable?

A. An extraneous variable259


C. A data set

D. A constant

103. Which of the following can best be described as a categorical

variable?

A. Age

B. Annual income


D. Religion

104. “Income distribution of employees” in a specific organization is an

example of which of following type of variable?





105. “There is no relationship between higher motivation level and higher

efficiency” is an example of which type of hypothesis?

A. Alternative

B. Null

C. Correlational

D. Research

106. Which of the following is not a role of hypothesis?

260





107. Which type of review compares how different theories address an issue?

A. Context review




108. After you locate a source, you should write down all details of the

reference, EXCEPT;

A. Volumes

B. Titles

C. Price


109. What is the primary focus of establishment surveys in this case study?

A. Collect the data through past studies

B. Analyze the literature review

C. Using of quantitative techniques

D. Data collection through mail and Interview

110. Which one of following is generally common in establishment survey and household survey?

A. Cognitive recall261

B. Homogenous respondents

C. Error free

D. Response burden


111. Which one of the following is not of important consideration in establishment survey while designing questionnaires?

A. Response burden

B. Professional terminology

C. Cognitive recall

D. Use of Records

112. Which of the following method of data collection is not discussed in the case study?

A. Questionnaires

B. Interviews

C. Mail survey

D. Observations

113. Which of the following sampling technique is used for Employee Turnover and Job Openings survey?


B. Cluster sampling

C. Stratified sampling

D. Convenience sampling

262

114. Which one of the following is the limitation of establishment survey in this case study?

A. Cost

B. Limited data

C. Unskilled interviewer

D. Small sample size

115. Which of the following is not the part of specific protocol of focus groups in ETJO?

A. Concept and indicators

B. Definition

C. Availability of records

D. Cognitive recall

116. Which of the following is the draw back of pretest interview in ETJO survey?

A. Small simple size

B. Non cooperative response

C. Probing

D. Questionnaire format

117. Which of the following method of data collection is not used in the case study?

A. Questionnaires

B. Focus groups

C. Correlational method

D. Secondary data

118. What is the basic purpose of ETJO survey?

263

A. To assess the feasibility of collecting job-vacancy and turnover data by

occupation

B. To analyze the problem of labor shortage

C. To assess the motivation level of employees

D. To analyze the factor contributing towards employee turnover

119. Which of the following is the basic purpose of pretest interview in this case study?

A. To identified the potential problem

B. To know the sample size

C. To develop the questionnaire

D. To use agency representative

120. Which one of the following sampling type is used in operations test to select the

units?



B. Cluster sampling

C. Quota sampling

D. Judgment sampling

121. Which of the following is the basic purpose of Response analysis survey in the case study?

A. To assess the quality of ETJO survey data

B. To know the sample size of ETJO survey data

C. To develop the questionnaire for ETJO

264

D. To use agency representative for ETJO

122. After Operation test, which of the following test findings were suggested by the

researcher?

A. Need of highly skilled and well trained interviewer

B. Sample size should be increased

C. A decent increase in survey budget

D. Focus group should be included

123. In which one of the following stage researcher consult the literature?

A. Operation test

B. Response analysis survey

C. Document design analysis

D. Pretest interviews

124. Which one of the following sampling type is used in Response analysis survey

(RAS)?


B. Cluster sampling

C. Quota sampling

D. Stratified sampling

125. Which one of the following could be helpful for minimizing the bias in this case

study?

A. Cognitive research

B. Focus group

265

C. Pretest Interview


126. Which one of the following is useful in assessing and clarifying concepts and

definitions at the beginning stages of questionnaire?

A. Operation test

B. Document design analysis

C. Focus group


127. Which one of the following can be more helpful than others in order to determine the exact source of measurement errors in establishment survey?

A. Focus group

B. Operation test

C. Response analysis survey

D. Document design analysis

Identify the ‘True’ and ‘False’ statements. (05)

13. Review of literature shows the incredibility of the body of knowledge and identifies the points at which the researcher made the research area ambiguous and unclear. (False)

14. The literature survey provides a solid foundation for developing the theoretical framework. (True)

15. The hypothesis should not only be specific to a place and situation but also these should be narrowed down with respect to its operation. (True )

16. A cohort analysis is similar to cross-sectional research. (False)


266

17. A literature review does not consider the prior studies, their agreements or disagreements in the field. (False)

Fill in the blanks with appropriate words.

1. Research hypothesis is formulated by the researcher which suggests the nature of relationship i.e. the direction of relationship.

2. Correlational hypothesis merely states that the variables occur together and does not imply that one causes the other.

3. Longitudinal type of research examine feature of any unit at more than one time.

4. Historical review traces the development of an idea or shows how a particular issue or theory has evolved over time.

5. Discontinuous variable is also known as discrete/ categorical/ classificatory variable.

6. Validity problems occur when the researcher’s theoretical definition does not

match that of the government agency or organization that collected the

information.

7. Reliability problems occur when official definition or the method of collecting

Information changes over time.

8. Secondary data refer to information gathered by someone other than the

researcher conducting the present study.

9. Experiments are best for topics where the researcher controls a situation and

manipulates an Independent variable.

10. A social indicator is any measure of wellbeing used in policy.

11.Two power bases of scientific knowledge are Empiricism and Rationalism

12.Action research is a type of Applied research

267

13.Three types of longitudinal research are time series, panel, and cohort

14.The research proposal is just like a research report, but it is written before the research project begins.

15.Natural science concepts are often expressed in symbolic forms.

16.The double blind experiment is designed to control experimenter expectancy.

17.Pilot testing is also called pre-testing.

18.The totality, out of which sample is drawn is referred to as population.

19.The physical setting of the interview creates Situational bias.

20.Probing is the verbal prompts made by field worker.

Long Questions:

268

Q1. Write any five similarities of Historical-Comparative research and Field

research?

Answer:

1. Both H-C research and field research recognize that the researcher’s point of view

is an avoidable part of research. Both involve interpretation, which introduce the

interpreter’s location in time, place, and world-view.

2. Both field and H-C research examine a great diversity of data. In both the

research becomes immersed in data to gain an emphatic understanding of events

and people.

3. Both field and H-C research often use grounded theory (theory usually emerges

during the process of data collection.)

4. Both field and H-C research involves a type of translation. The researcher’s

meaning system usually differs from that of people he or she studies, but he or she


tries to penetrate and understand their point of view.

5. Both field and H-C research focus on action, process, and sequence and see time

process as essential.

6. Generalization and theory are limited in field and H-C research.

Q2. How quantitative and qualitative techniques are applied in Historical-

Comparative research.

Answer:

Quantitative approach

The quantitative techniques with some minor adjustment can be applied to study the past

or other cultures.269

The researcher can focus on the issue in one society, few societies or multiple

societies.

The researcher can focus on the issue in one time in the past or examine the issue

across many years/periods in the past.

The researcher can focus on the issue in the present or a recent past period.

The researcher’s analysis could be based primarily on quantitative data or

qualitative data.

Qualitative approach

The researcher must be able to take on, mentally, the circumstances, views, and

feelings of those being studied to interpret their action appropriately.

The historical-comparative research must find patterns among the voluminous

details describing the subject matter of study.

Question # 01

How do concrete and abstract concepts differ? Give example.

(Marks: 04)

Solution:

Concrete Concepts:

Concrete ones refer to straightforward physical objects or familiar experiences.

Abstract concepts:

Abstract concepts refer to ideas that have a scattered meaning or an indirect expression Abstraction is a thought process wherein ideas are distanced from objects.

270

The difference between concrete and abstract concepts can be expressed with some characterizations like,

c) Abstract concepts have only relational properties while concrete concepts have some fundamental properties.

d) Abstract concepts are universals and concrete concepts are particulars.e) Abstract concepts are sets (generalized) and concrete concepts are individuals

(specified).f) Concrete concepts are known by observation whereas abstract concepts are known

in some other way, e.g., by abstraction, by intuition, etc

Example

Print Media (Abstract)

Publication

News Paper

Daily Dawn (Concrete)

Question # 02


Given the situation below, Discuss with reason into which category they fall

According to the purpose of doing research and The uses of research

(Marks: 03, 03)

271

Scenario 1:

Reasons for Absenteeism

A university professor wanted to analyze in depth the reasons for absenteeism of employees in organizations. Fortunately, a company within 20 miles of the campus employed her as a consultant to study that very issue.

Solution:

According to the purpose of doing research :It is Explanatory research as the purpose is to find out the reasons for a phenomenon i.e. absenteeism of employees in organizations. Research seeks to determine the answers to why question about a specific behavior.

According to the uses of research:It is applied research since, the problem is being faced by an organization and the research is called upon to solve it.

Scenario 2:

Effects of Nasal Spray on Flu

A research scientist surveys 1,000 employees in different organizational settings to study the efficacy of several types of nasal sprays in controlling the flu virus. He subsequently publishes his findings in a highly respected medical journal.

Solution:

According to the purpose of doing research :It is Descriptive research, as, the research question only finds out the special effects of several types of nasal sprays in controlling the flu virus in different organizational settings. It is to find out the relationship among the substances under study.

272

According to the uses of research:It is a Basic research since the underlying purpose is to expand the frontier of knowledge

.

Question#01:

Why turn over is high in some organizations?

As per above given query, explain the following components of Theoretical frame work; (Marks: 10)

Develop an inventory of variables (min. five variables required) Specify direction of relationship Give clear explanation why you should expect the proposed relationship exists Make an inventory of propositions

Ans:

Develop an inventory of variables

Salary Package is low, Inflexibility in working hours, Low decentralization (participation in decision making), Lack of other benefits (bonus, appraisals, conveyance facilities, etc), Poor working ambiance

Specify direction of relationship

Between salary & turn-over negative relationship exists Between flexible working hours & turn-over negative relationship exists Between decentralization & turn-over negative relationship exists


Between extra benefits & turn-over negative relationship exists Between ambiance & turn-over negative relationship exists

273

Give clear explanation why you should expect the proposed relationship exists?o Between salary & turn-over negative relationship exists because in current era

a good salary package has more attraction for employees to remain in the same organization. So organizations that keep themselves up-dated with privileged market salary packages usually have low turn over ratio.

o Between flexible working hours & turn-over negative relationship exists because flexibility in working hours give some relaxation to employees especially in case when their targets are not achieved due to a reason able fact.

o Between decentralization & turn-over negative relationship exists because participation in decision making raise confidence of employee and motivation level. So, organization have more decentralized system face low turn-over ratio.

o Between extra benefits & turn-over negative relationship exists. The organizations offer different packages like bonuses, conveyance facilities etc, such organizations have more satisfies employees and low turn over.

o Between ambiance & turn-over negative relationship exists. Working ambiance does matter a lot. Good ambiance that help in releasing working stress increase the employee motivation and interest in doing job well.

Question#02:

What is meant by a Research Proposal? Explain briefly. Also mention at what time a research proposal is submitted? (Marks: 05)

Note: (Copied data from hand outs will not be appreciated)

Ans:

A research proposal is a document that plans how and in which manner a research will be conducted. Research proposals contain extensive literature reviews. Such proposals must offer convincing support for your research topic. It means the topic/issue for which research study is being proposed should be sound enough to conduct a worthy research. The proposal must describe a detailed methodology for conducting the research i.e. which tools are going to be used in your research.

More over when writing a proposal it is well to assume that reader of your proposal is interested to find out the answer of these questions;

a. What do you want to do, how much will it cost, and how much time will it take?

b. What has already been done in the area of your project? c. How do you plan to do it?

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d. How will the results be evaluated?

A good proposal is that which well defines these questions and convinces the reader that research on specified issue is needed to conduct. So, the research proposal is submitted before starting the research project because in this you plan how the data will be collected and analyzed.

Q. Explain the difference between these terms with one example of each.

i. Population and target population

ii. Sampling unit and observation unit

iii. Parameter and statistic

i. Population and Target Population.

Population refers to the entire group of people, events or things of interest that the

researcher wishes to investigate.

Target population is the complete group of specific population elements relevant to the

research project.

Example

Suppose a researcher wants to investigate the productivity of employees working in

multinationals in Pakistan.

All the employees working in multinational will be the population.

The researcher wants to investigate the productivity of employees working in

multinational in FMCG sector in Pakistan.


All the employees working in multinationals in FMCG sector in Pakistan will be the

target population.

ii. Sampling Unit and Observation Unit

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A sampling unit is that element or set of elements considered for selection in some stage

of sampling.

An observation unit is an element or aggregation of elements from which the

information is collected.

Example

In the above example the researcher selects employees from three FMCG multinationals

(Procter and Gamble, Unilever and Nestle) for data collection. Among these employees

he selected First Line Managers for collecting the data. Among all First Line Manager he

selects 40 Line managers for data collection.

In this example the employees from three FMCGs (Procter and Gamble, Unilever and

Nestle) are the primary sampling unit, all the First Line managers are the secondary/ final

sampling unit and the selected First Line managers are the observation unit.

iii. Parameter and Statistics

A parameter is the summary description of a given variable in a population while

Statistic is the summary description of a given variable in a survey sample.

Example

In the above example the mean productivity of all the employees working in the

multinational is the Parameter and the mean productivity of the First Line managers from

those the researcher collected the data is the Statistics.

Q: Define Research? Discuss the special features of Scientific method of Research?

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Solution:

Definition of Research:

Research is an organized and systematic way of finding answers to questions by gathering the needed information. General image of the research is that it has something to do with the laboratory where scientists are supposedly doing some experiments. Research is simply the process of finding solutions to a problem after thorough study and analysis of the situational factors. In research, we try to follow a system or a procedure in an organized manner. It is all the more necessary in case we want to repeat the study, or somebody else wants to verify our findings. In the latter case the other person has to follow the same procedure that we followed. Hence not only we have to do the study in a systematic manner but also that system should be known to others.

Special Features of Scientific Method of Research:

The Scientific method of Research is a procedure to produce knowledge and to discover the principles & laws in this universe.

Special Features of Scientific Method of Research are as follows:

1. Empirical

Scientific method is concerned with the realities that are observable through “sensory experiences.” It generates knowledge which is verifiable by experience or observation. Some of the realities could be directly observed, like the number of students present in the class and how many of them are male and how many female. The same students have attitudes, values, motivations, aspirations, and commitments. These are also realities which cannot be observed directly, but the researchers have designed ways to observe these indirectly. Any reality that cannot be put to “sensory experience” directly or indirectly (existence of heaven, the Day of Judgment, life hereafter, God’s rewards for good deeds) does not fall within the domain of scientific method.

2. Verifiable

Observations made through scientific method are to be verified again by using the senses to confirm or refute the previous findings. Such confirmations may have to be made by the same researcher or others. We will place more faith and credence in those findings and conclusions if similar findings emerge on the basis of data collected by other researchers using the same methods. To the extent that it does happen (i.e. the results are replicated or repeated) we will gain confidence in the scientific nature of our research. Replicability, in this way, is an important characteristic of scientific method. Hence revelations and intuitions are out of the domain of scientific method.

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3. Cumulative

Prior to the start of any study the researchers try to scan through the literature and see that their study is not a repetition in ignorance. Instead of reinventing the wheel the researchers take stock of the existing body of knowledge and try to build on it. Also the researchers do


not leave their research findings into scattered bits and pieces. Facts and figures are to be provided with language and thereby inferences drawn. The results are to be organized and systematized. Nevertheless, we don’t want to leave our studies as stand alone. A linkage between the present and the previous body of knowledge has to be established, and that is how the knowledge accumulates.

4. Deterministic

Science is based on the assumption that all events have antecedent causes that are subject to identification and logical understanding. For the scientist, nothing “just happens” – it happens for a reason. The scientific researchers try to explain the emerging phenomenon by identifying its causes. Of the identified causes which ones can be the most important? For example, in the 2006 BA/BS examination of the Punjab University 67 percent of the students failed. What could be the determinants of such a mass failure of students? The researcher may try to explain this phenomenon and come up with variety of reasons which may pertain to students, teachers, administration, curriculum, books, examination system, and so on. Looking into such a large number of reasons may be highly cumbersome model for problem solution. It might be appropriate to tell, of all these factors which one is the most important. The researcher tries to narrow down the number of reasons in such a way that some action could taken.

5. Ethical and Ideological Neutrality

The conclusions drawn through interpretation of the results of data analysis should be objective; that is, they should be based on the facts of the findings derived from actual data, and not on our own subjective or emotional values. For instance, if we had a hypothesis that stated that greater participation in decision making will increase organizational commitment, and this was not supported by the results, it makes no sense if the researcher continues to argue that increased opportunities for employee participation would still help. Such an argument would be based, not on the factual, data based research findings, but on the subjective opinion of the researcher. If this was the conviction of the researcher all along, then there was no need to do the research in the first place. Researchers are human beings, having individual

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ideologies, religious affiliations, cultural differences which can influence the research findings. Any interference of their personal likings and dis-likings in their research can contaminate the purity of the data, which ultimately can affect the predictions made by the researcher. Therefore, one of the important characteristics of scientific method is to follow the principle of objectivity, uphold neutrality, and present the results in an unbiased manner.

6. Statistical Generalization

Generalisability refers to the scope of the research findings in one organizational setting to other settings. Obviously, the wider the range of applicability of the solutions generated by research, the more useful the research is to users. For instance, if a researcher’s findings that participation in decision making enhances organizational commitment are found to be true in a variety of manufacturing, industrial, and service organizations, and not merely in the particular organization studied by the researcher, the generalisability of the findings to other organizational settings is enhanced. The more generalizable the research, the greater its usefulness and value.

For wider generalisability, the research sampling design has to be logically developed. Here the use of statistics is very helpful. Statistics is device for comparing what is observed and what is logically expected. The use of statistics becomes helpful in making generalizations, which is one of the goals of scientific method.

7. Rationalism

Science is fundamentally a rational activity, and the scientific explanation must make sense. Religion may rest on revelations, custom, or traditions, gambling on faith, but science must rest on logical reason. There are two distinct logical systems important to the scientific quest, referred to as deductive logic and inductive logic.

Q: Define Hypothesis? What are different types of hypothesis? Explain.

Solution:

Definition of Hypothesis:

A proposition that can be verified to determine its reality is a hypothesis. A hypothesis may be defined as a logically conjectured relationship between two or more variables, expressed in the form of a testable statement. Relationship is proposed by using a strong logical argumentation. This logical relationship may be part of theoretical framework of the study.

For example,

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a. Officers in my organization have higher than average level of commitment (variable).

b. Level of job commitment of the officers is associated with their level of efficiency.c. Level of job commitment of the officers is positively associated with their level of

efficiency.Research Method (STA 630) Success Objectives

d. The higher the level of job commitment of the officers the lower their level of absenteeism.

Types of Hypothesis:

There are different types of hypothesis which are as follows.

1-Descriptive Hypothesis

Descriptive hypothesis contains only one variable thereby it is also called as univariate hypothesis. Descriptive hypotheses typically state the existence, size, form, or distribution of some variable. The first hypothesis contains only one variable. It only shows the distribution of the level of commitment among the officers of the organization which is higher than average. Such a hypothesis is an example of a Descriptive Hypothesis.

2- Relational Hypothesis

These are the propositions that describe a relationship between two variables. The relationship could be non-directional or directional, positive or negative, causal or simply correlational.

While stating the relationship between the two variables, if the terms of positive, negative, more than, or less than are used then such hypotheses are directional because the direction of the relationship between the variables (positive/negative) has been indicated. These hypotheses are relational as well as directional. The directional hypothesis is the one in which the direction of the relationship has been specified.

Non-directional hypothesis is the one in which the direction of the association has not been specified. The relationship may be very strong but whether it is positive or negative has not been postulated.

Correlational hypotheses state merely that the variables occur together in some specified manner without implying that one causes the other. Such weak claims are often made when we believe that there are more basic causal forces that affect both variables. For example:

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Explanatory (causal) hypotheses imply the existence of, or a change in, one variable causes or leads to a change in the other variable. This brings in the notions of independent and the dependent variables. Cause means to “help make happen.” So the independent variable may not be the sole reason for the existence of, or change in the dependent variable.

3- Null Hypothesis

It is used for testing the hypothesis formulated by the researcher. Researchers treat evidence that supports a hypothesis differently from the evidence that opposes it. They give negative evidence more importance than to the positive one. It is because the negative evidence tarnishes the hypothesis. It shows that the predictions made by the hypothesis are wrong. The null hypothesis simply states that there is no relationship between the variables or the relationship between the variables is “zero.” That is how symbolically null hypothesis is denoted as “H0”. For example:

H0 = There is no relationship between the level of job commitment and the level of efficiency. Or

H0 = The relationship between level of job commitment and the level of efficiency is zero. Or the two variables are independent of each other.

It does not take into consideration the direction of association (i.e. H0 is non directional), which may be a second step in testing the hypothesis.

4- Alternative Hypothesis

The alternative (to the null) hypothesis simply states that there is a relationship between the variables under study. In our example it could be: there is a relationship between the level of job commitment and the level of efficiency. Not only there is an association between the two variables under study but also the relationship is perfect which is indicated by the number “1”. Thereby the alternative hypothesis is symbolically denoted as “H1”. It can be written like this:

H1: There is a relationship between the level of job commitment of the officers and their level of efficiency.

5- Research Hypothesis

Research hypothesis is the actual hypothesis formulated by the researcher which may also suggest the nature of relationship i.e. the direction of relationship. In our example it could be:

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Q: Ahmad is the manager of a restaurant; he wants to see his staff cooperative and hardworking but his staff is not working well according to his will. He decided to give the incentives in order to motivate and encourage them but his policy did not work effectively. There can be many factors behind this behavior of staff that needs to be researched. For this purpose, he appoints you as a researcher and asks you to discover those factors and submit a report to him. How you will undertake this kind of


research and what steps you will choose to make a report about the behavior of the staff?

Solution:

The manager of the restaurant appoints me as a researcher to find out the factors behind the staff behavior. I will take the following steps in order to undertake this research and to make a report. These steps are as follows:

STEP 1: To Select the topic of research:

First of all I will select the topic which is a general area of study or issue. The topic in this research is the factors behind the staff behavior. A topic appears to be too broad for conducting research. The specific issues that need to be researched within the situation may not be identified at this stage. I will try to analyze the problems currently existing in the restaurant that needs to be solved and the areas that a manager believes need to be improved in the restaurant (improving the existing policies). Then I will develop some research questions that a basic researcher wants to answer empirically.

STEP 2: Preliminary Data Collection or to Explore different areas from where I can get information related to the restaurant and staff behavior:

After selecting the topic, I will collect data from different sources. This step may be considered as part of the exploratory research. An exploration typically begins with a search for published data and studies. Such sources can provide secondary data which becomes part of the background information (about the restaurant & groups of people). Some secondary sources of data are statistical bulletins, government publications, information published or unpublished, case studies, online data, web

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sites, and the Internet from where I can get information. In addition, information can also be collected from the people who are well informed about the staff and restaurant, especially those who have clearly stated positions on controversial aspects of the problem. In certain situations, I will also focus on group discussions with the staff of the restaurant. Such discussions can help me in the identification of factors and having clarification of their behavior.

STEP 3: Problem Definition

After having discussions with the professionals as well as with the staff to whom the issue relates, and the review of literature, now I will be in a position to narrow down from its original broad base and define the factors clearly. Translate the broad issue into a research question. As part of the applied research convert the management dilemma into a management question, and then on to research question that fits the need to resolve the dilemma. The symptoms of a problem might help tracing the real problem. For example in this research, the productivity decline of workers is an issue. The manager has tried to solve it by the provision of incentives but his policy did not work. I will find the possible factors like the morale and motivation of the workers having some other antecedents.

STEP 4: To develop the Theoretical Framework

Consultations with the informants and professionals, and the review of literature will help me in the identification of different factors that are considered to be relevant. Now I will need to make a logical relationship among several factors identified. This will help in the delineation of the theoretical framework. The theoretical framework discusses the interrelationships among the variables that are deemed to be integral to the dynamics of the situation being investigated. Developing such a conceptual framework helps to postulate or hypothesize and test certain relationships.

STEP 5: To Generate the Hypotheses

Once I have identified the important variables relevant to an issue and established the logical reasoning in the theoretical framework, I will be in a position to test whether the relationships that have been theorized do in fact hold true. By testing these relationships scientifically, I will obtain reliable information to determine the relationship among the variables. The results of these tests offer part of the answers to the formulated research questions, whether these relate basic research or to applied research.

STEP 6: To make a Research Design

Research design is a master plan specifying the methods and procedures for collecting and analyzing the needed information. It is a framework or the blueprint that plans the action for research project. The objectives of the study determined during the

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early stages of the research are included in the design to ensure that the information collected is appropriate for solving the problem. It is very important to specify the sources of information, and the research method or technique (survey or experiment, for example) to be followed in the study. Broadly there are six basic research methods for descriptive and causal research: surveys, experiments, observation, communication analysis (content analysis), case study, focus group discussion.

STEP 7: Data Collection, Data Processing, and Analysis


Data collection is integral part of the research design; Data collection is determined by the research technique selected for the project. Data can be collected in a variety of ways, in different settings – field or lab – and from different sources. It could include interviews – face to face interviews, telephone interviews, computer-assisted interviews, and interviews through electronic media; questionnaires that either personally administered, sent through mail, or electronically administered; observation of individuals and events which could be participant or non participant. Once the fieldwork has been completed, the data must be converted into a format that will answer the research questions and help testing the hypotheses. The computer can help in making tables and the application of different statistics.

STEP 8: Testing the Hypotheses; Answering the Research Questions

The analysis and interpretation of the data shall be the means to testing the formulated hypotheses as well as finding answers to the research questions. In case of applied research, the research should be helpful in finding solutions to the problems of the organization or society. Making recommendations may also be part of this process.

STEP 9: Report Writing

The research report should communicate the research findings effectively. All too often the report is a complicated statement of the study’s technical aspects and sophisticated research methods. The report has to be presented in the format as it may have been part of the terms of reference if it is a sponsored study. I will write the basic factors behind the staff behavior in my report and I will also give some suggestions to the manager to motivate the staff so that they can work efficiently.

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Q: Define the measure that is used by the researcher in order to capture the intensity, direction, level, or potency of a variable construct. Also describes the different types of that measure.

Solution:

The measure that is used by the researcher in order to capture the intensity, direction, level, or potency of a variable construct:

A scale is a measure in which a researcher captures the intensity, direction, level, or potency of a variable construct. It arranges responses or observations on a continuum or in series of categories. A scale can use a single indicator or multiple indicators.

An index is a measure in which a researcher adds or combines several distinct indicators of a construct into a single score. The composite scores is often a simple sum of the multiple indicators. Indexes are often measured at the interval or ratio level.

Researchers sometimes combine the features of scales and indexes in a single measure. This is common when a researcher has a several indicators that are scales (i.e. that measure intensity or direction). The researcher then adds these indicators together to yield a single score, thereby creating an index.

The different types of that measure:

A scale refers to any series of items that are arranged progressively according to value or magnitude, into which an item can be placed according to its quantification. In other words, a scale is a continuous spectrum or series of categories.

It is traditional to classify scales of measurement on the basis of the mathematical comparisons that are allowable with these scales. Four types of scales are nominal, ordinal, interval, and ratio.

Nominal Scale

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A nominal scale is the one in which the numbers or letters assigned to objects serve as labels for identification or classification. This measurement scale is the simplest type. With nominal data, we are collecting information on a variable that naturally or by design can be grouped into two or more categories that are mutually exclusive, and collectively exhaustive.

Nominal scales are the least powerful of the four scales. They suggest no order or distance relationship and have no arithmetic origin. Nevertheless, if no other scale can be used, one can almost always one set of properties into a set of equivalent classes.

Ordinal Scale


Ordinal scales include the characteristics of the nominal scale plus an indicator of order. If a is greater than b and b is greater than c, then a is greater than c. The use of ordinal scale implies a statement of “greater than” or “less than” without stating how much greater or less. Other descriptors can be: “superior to,” “happier than,” “poorer than,” or “above.”

Interval Scale

Interval scales have the power of nominal and ordinal scales plus one additional strength: they incorporate the concept of equality of interval (the distance between 1 and 2 equals the distance between 2 and 3). For example, the elapsed time between 3 and 6 A. M. equals the time between 4 and 7 A. M. One cannot say, however, 6 A.M. is twice as late as 3 A.M. because “zero time” is an arbitrary origin. In the consumer price index, if the base year is 1983, the price level during 1983 will be set arbitrarily as 100. Although this is an equal interval measurement scale, the zero point is arbitrary.

Ratio Scale

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Ratio scales incorporate all the powers of the previous scales plus the provision for absolute zero or origin. Ratio data represent the actual amounts of variable. Measures of physical dimensions such as weight, height, distance, and area are the examples. The absolute zero represents a point on the scale where there is an absence of the given attribute. If we hear that a person has zero amount of money, we understand the zero value of the amount.

Q: (a) Define the Probability & non-Probability sampling.

Solution (a):

Probability Sampling:

In probability sampling, every element in the population has a known nonzero probability of selection. The simple random is the best known probability sample, in which each member of the population has an equal probability of being selected.

Non-Probability Sampling:

In non-probability sampling the probability of any particular element of the population being chosen is unknown. The selection of units in non-probability sampling is quite arbitrary, as researchers rely heavily on personal judgment.

(b) “Snowball sampling is also known as network, chain referral or reputational sampling.” Comment on this statement.

Solution (b):

Snowball sampling:

Snowball sampling is also called network, chain referral, or reputational sampling. It is a method for identifying and sampling cases in the network. It is based on an analogy to a snowball, which begins small but becomes larger as it is rolled on wet snow and picks up additional snow. It begins with one or a few people or cases and spreads out on the basis of links to the initial cases.

This design has been found quite useful where respondents are difficult to identify and are best located through referral networks. In the initial stage of snowball sampling, individuals are discovered and may or may not be selected through probability methods. This group is then used to locate others who possess similar

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characteristics and who, in turn, identify others. The “snowball” gather subjects as it rolls along.

Example:

For example, a researcher examines friendship networks among teenagers in a community. He or she begins with three teenagers who do not know each other. Each teen names four close friends. The researcher then goes to the four friends and asks each to name four close friends, then goes to those four and does the same thing again, and so forth. Before long, a large number of people are involved. Each person in the sample is directly or indirectly tied to the original teenagers, and several people may have named the same person. The researcher eventually stops, either because no new names are given, indicating a closed network, or because the network is so large that it is at thee limit of what he or she can study.

(c)The purpose of cluster sampling is to sample economically while retaining the characteristics of a probability sample. At the same time, cluster sampling addresses two major problems. Discuss those problems.


Solution (c):

The purpose of cluster sampling is to sample economically while retaining the characteristics of a probability sample. At the same time, Cluster sampling addresses following two problems:

1. Researchers lack a good sampling frame for a dispersed population and the cost to reach a sampled element is very high. A cluster is unit that contains final sampling elements but can be treated temporarily as a sampling element itself. A researcher first samples cluster, each of which contains elements, then draws a second sample from within the clusters selected in the first stage of sampling. In other words, the researcher randomly samples clusters, and then randomly samples elements from within the selected clusters. He or she can create a good sampling frame of clusters, even if it is impossible to create one for sampling elements. Once the researcher gets a sample of clusters, creating a sampling frame for elements within each cluster becomes more manageable.

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2. A second advantage for geographically dispersed populations is that elements within each cluster are physically closer to each other. This may produce a savings in locating or reaching each element.

Q: Briefly discuss the steps that are involved in conducting an experiment.

Solution:

Steps in Conducting an Experiment

Broadly there are about 12 steps in conducting an experiment, which are as below:

Make a hypothesis that is appropriate for experimental research. Decide about an experimental design that will test the hypothesis within practical

limitations. Decide how to create a situation that induces the independent variable. Develop a valid and reliable measure of the dependent variable. Set up an experimental setting and conduct a pilot test of the treatment and

dependent variable measures. Locate appropriate subjects or cases. Randomly assign subjects to groups and give careful instructions. Gather data for the pretest measure of the dependent variable for all groups. Introduce the treatment to the experimental group only (or to the relevant groups if

there are multiple experimental groups) and monitor all groups. Gather data for posttest measure of the dependent variable. Debrief the subjects by informing them of the true purpose and reasons for the

experiment. Ask subjects what they thought was occurring. Examine data collected and make comparisons between different groups. Where

appropriate, use statistics and graphs to determine whether or not the hypothesis is supported.

Q. Classify this research on the basis of:

Purpose of doing research. The use of research Time dimension in researchJustify your answer.

Answer:

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It is an exploratory research. Because it was a new issue and no research was made on it before. The researchers had limited amount of information on this issue and this research provided bases for many other studies.

It is a basic research because it provides knowledge generated to understand a phenomenon of interest to the researcher.

It is a longitudinal research because it examines the employees at more than one time. The research is spread upon 1927 to 1932. A group of 6 women was selected for 5 years so it can be further classified as Panel study.


Q. Identify these variables used in the experiment:

Dependent variablesIndependent variablesExtraneous variables

Justify your answer.

Answer:

The variable that is the result of another variable(s) is called a dependent variable. Productivity of the employees is the dependent variable in this case. Because it depends on many other independent variables.

The variable that causes the dependent variable is called independent variable. It is a cause variable. In our example light illumination, rest breaks, duration of work hours, temperature, food, wages and humidity are independent variables because they affect productivity.

Extraneous variables are factors other than the independent variable that could result in changes in the dependent variable. In an experiment, these factors should be controlled so that they are constant in all conditions. If they are not well-controlled, then they result in possible alternative explanations (other than changes in the independent variable) that could account for the changes observed in the dependent variable. Possible extraneous variables in this research can be knowledge of the employees that they are being observed (when employees know that they are being watched, they tend to modify their behavior), special attention paid to them, supervisor’s style, etc.

Q: What do you understand by the term “concepts are an abstraction of reality”? Explain with the help of an example.

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Answer: Concepts are the terms and terminologies used by researchers as means of communication. They are expressed in words, letters, signs and symbols that refer to various events or objects. Abstraction simply means “generalization.” In research methods, we use this term “concepts are an abstraction of reality”. It means that we pick up concepts from observed reality and goes on to the abstraction level. It is a level at which objects and events are expressed in more generalized form.

For example Toyota is a concept, its abstraction is a car and its further abstraction would be motor vehicles. We have changed the simple concept (Toyota) into an abstraction (motor vehicles) which is a more generalized term.

Q: Join the options in column A with appropriate options given in column B. Identify the variables and give reasons for your choice.

Column A Column B

Two men and three women were seriously injured in a road accident 25 km away from Lahore.

(i) Intervening variable

Out break of Malaria in the city increased the consumption of mosquito repellents.

(ii) Independent and dependent variable

Distance learning system increased the literacy level in the country.

(iii)Continuous and discontinuous variable

Answer:

Column A Column B

(a) (iii)

(b) (ii)

(c) (i)


Identification of Variables:

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Men and Women are the example of discontinuous variables and the distance of 25 km is an example of continuous variable.‘Out break of malaria’ is the independent variable and ‘increase in the purchase of mosquito repellents’ is dependent variable.There is a clear indication of many intervening variable such as flexible timing, low fees, low transportation cost, easy access to get education especially for far off areas.

Reasons:

Discontinuous variable has limited number of distinct values which can not be divided into fractions, so male/female or men/women are discontinuous variables. Continuous variable can take infinite number of values and can be divided into fractions, so the distance is continuous variable as it can take any value e.g. 35km, 55.5 km etc.Independent variables are those variables which identifies forces or conditions that act on something. Malaria is the independent variable as it is causing change in other variable. Dependent variables are the effect or result of another variable. Their occurrence is dependent upon the occurrence of another variable. Increase in the consumption of mosquito repellents is an outcome of increasingly spreading Malaria disease. Intervening variables are those variables that come between independent and dependent variables and shows a link or mechanism between them. Distance learning (independent variable) has increased the literacy level (dependent variable) and there are other intervening variables which are supporting this relationship e.g. flexible timing, low fees, low transportation cost, easy access to get education especially for far off areas.

MIDTERM EXAMINATIONSTA301- Statistics and Probability (Session - 2)Question No: 1 ( Marks: 1 ) - Please choose oneMedian can be found only when:Data is DiscreteData is AttributedData is continuousData is continuousData is attributedData is arrangedQuestion No: 2 ( Marks: 1 ) - Please choose oneFrom the following observations 2,3,4,5,4,6,4, the mode is:2345Question No: 3 ( Marks: 1 ) - Please choose oneHow to construct the class interval:Divide the class frequencies in half

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Divide the class frequency by the number of observationsFind the difference between consecutive lower class limitsCount the number of observations in the classQuestion No: 4 ( Marks: 1 ) - Please choose oneHow many elements are in the sample space of rolling one die:6122436Question No: 5 ( Marks: 1 ) - Please choose oneWhen two coins are tossed the probability of at most one head is:1/42/43/44/4Question No: 6 ( Marks: 1 ) - Please choose oneIf A and B are mutually exclusive events then P(AB or ) equals:P A ( )P +B ( )P (A aBnd )P A (P)B ( )P A ( )P +B ( )P (A|B)P+ A(B| )Question No: 7 ( Marks: 1 ) - Please choose oneIn scatter diagram the variable plotted along Y-axis is:Independent variableDependent variableAny oneUndefinedQuestion No: 8 ( Marks: 1 ) - Please choose onePositive square root of variance of a distribution is:RangQuartile deviationStandard deviationonly (a) &(c)Question No: 9 ( Marks: 1 ) - Please choose oneWhen more values are lying at the start of the distribution, it is a:Symmetrical distributionPositively skewedNegatively skewedU shape figureQuestion No: 10 ( Marks: 1 ) - Please choose oneWhat is ‘m f’ in the formula of mode:First frequencyLast frequencyMaximum frequencyMinimum frequencyQuestion No: 11 ( Marks: 1 ) - Please choose one

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If median = 7 and Mean = 5, what is the value of2 Q:1357Question No: 12 ( Marks: 1 ) - Please choose oneThe probability of drawing a king of spade from a pack of 52 cards is:1/41/131/261/52Question No: 13 ( Marks: 1 ) - Please choose oneWhen referring to a curve whose longer tail is to the left, you would call it:U shapeSkewed to the leftSkewed to the rightSymmetricalQuestion No: 14 ( Marks: 1 ) - Please choose oneIn statistics,we deal with:IndividualsIsolated itemsAggregates of factsQualitative dataQuestion No: 15 ( Marks: 1 ) - Please choose oneWhen data is labeled to identify an attribute of element, the measurement scale is:OrdinalIntervalNominalRatioQuestion No: 16 ( Marks: 1 ) - Please choose oneThe distribution is mesokurtic if the Moment Coefficient of kurtosis2 bis:

MIDTERM EXAMINATIONSTA301- Statistics and Probability (Session - 2)Question No: 1 ( Marks: 1 ) - Please choose oneA histogram consists of a set of adjacent rectangles whose bases are marked off by:Class boundariesClass limitsClass marksClass frequencyQuestion No: 2 ( Marks: 1 ) - Please choose oneStem and leaf was introduced by:Francis Galton

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FriedmanJohn TukeyPearsonQuestion No: 3 ( Marks: 1 ) - Please choose oneFor positively skewed distributionMean…….Median…….Mode:=<>Question No: 4 ( Marks: 1 ) - Please choose oneFor a positively skewed distribution:Mean<Mode<MedianMdian<Mode>MeanMode>Mean>MedianMean>Median>ModeQuestion No: 5 ( Marks: 1 ) - Please choose oneC equals 5

5:151025Question No: 6 ( Marks: 1 ) - Please choose oneIf a curve has a longer tail to the right, it is called :Positively skewednegatively skewedJ-shapedsymmetricQuestion No: 7 ( Marks: 1 ) - Please choose oneIn measures of relative dispersion unit of measurement is:ChangedVanishDoes not changedDependentQuestion No: 8 ( Marks: 1 ) - Please choose oneData used by an agency which is originally collected by them is :Primary dataRaw dataSecondary dataGrouped dataQuestion No: 9 ( Marks: 1 ) - Please choose oneWhen we toss a coin , we get only:1 outcome2 outcomes3 outcomes4 outcomesQuestion No: 10 ( Marks: 1 ) - Please choose one

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Which of the following is the class frequencyThe number of observations in each classThe difference between consecutive lower class limitsAlways contains at least 5 observationsUsually a multiple of the lower limit of the first classQuestion No: 11 ( Marks: 1 ) - Please choose oneStandard deviation is affected by the change of________:Origin & scaleOrigin onlyScale onlyNot origin & scaleQuestion No: 12 ( Marks: 1 ) - Please choose oneFor a moderately skewed distributions, the approxi mate percentage of case includedbetween X 2S and X 2S is :99.7%68%95%50%Question No: 13 ( Marks: 1 ) - Please choose oneA die is rolled. What is the probability that the number rolled is greater than 2 and even:1/21/32/35/6Question No: 14 ( Marks: 1 ) - Please choose oneThe probability of drawing any one spade card is:1/524/5213/5252/52Question No: 15 ( Marks: 1 ) - Please choose oneWhich of the following is not the type of frequency curves?The symmetrical frequency curveThe extremely skewed frequency curveThe U-shaped frequency curveFrequency polygonQuestion No: 16 ( Marks: 1 ) - Please choose oneIf the third moment about mean is zero( m3 0), then the distribution is:Symmetrical

MIDTERM EXAMINATIONSTA301- Statistics and Probability (Session - 2)

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Question No: 1 ( Marks: 1 ) - Please choose oneA histogram consists of a set of adjacent rectangles whose bases are marked off by:Class boundariesClass limitsClass marksClass frequencyQuestion No: 2 ( Marks: 1 ) - Please choose oneStem and leaf was introduced by:Francis GaltonFriedmanJohn TukeyPearsonQuestion No: 3 ( Marks: 1 ) - Please choose oneFor positively skewed distributionMean…….Median…….Mode:=<>Question No: 4 ( Marks: 1 ) - Please choose oneFor a positively skewed distribution:Mean<Mode<MedianMdian<Mode>MeanMode>Mean>MedianMean>Median>ModeQuestion No: 5 ( Marks: 1 ) - Please choose oneC equals 5

5:151025Question No: 6 ( Marks: 1 ) - Please choose oneIf a curve has a longer tail to the right, it is called :Positively skewednegatively skewedJ-shapedsymmetricQuestion No: 7 ( Marks: 1 ) - Please choose oneIn measures of relative dispersion unit of measurement is:ChangedVanishDoes not changedDependentQuestion No: 8 ( Marks: 1 ) - Please choose oneData used by an agency which is originally collected by them is :Primary dataRaw data

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Secondary dataGrouped dataQuestion No: 9 ( Marks: 1 ) - Please choose oneWhen we toss a coin , we get only:1 outcome2 outcomes3 outcomes4 outcomesQuestion No: 10 ( Marks: 1 ) - Please choose oneWhich of the following is the class frequencyThe number of observations in each classThe difference between consecutive lower class limitsAlways contains at least 5 observationsUsually a multiple of the lower limit of the first classQuestion No: 11 ( Marks: 1 ) - Please choose oneStandard deviation is affected by the change of________:Origin & scaleOrigin onlyScale onlyNot origin & scaleQuestion No: 12 ( Marks: 1 ) - Please choose oneFor a moderately skewed distributions, the approxi mate percentage of case includedbetween X 2S and X 2S is :99.7%68%95%50%Question No: 13 ( Marks: 1 ) - Please choose oneA die is rolled. What is the probability that the number rolled is greater than 2 and even:1/21/32/35/6Question No: 14 ( Marks: 1 ) - Please choose oneThe probability of drawing any one spade card is:1/524/5213/5252/52Question No: 15 ( Marks: 1 ) - Please choose oneWhich of the following is not the type of frequency curves?The symmetrical frequency curveThe extremely skewed frequency curveThe U-shaped frequency curveFrequency polygonQuestion No: 16 ( Marks: 1 ) - Please choose oneIf the third moment about mean is zero

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( m3 0), then the distribution is:Symmetrical

MIDTERM EXAMINATIONSTA301 - STATISTICS AND PROBABILITY (Session - 4)Marks: 30Time: 60minStudentID/LoginID: ______________________________Student Name: ______________________________Center Name/Code: ______________________________Exam Date: Monday, June 05, 2006Please read the following instructions carefully before attempting any of thequestions:1. Attempt all questions. Marks are written adjacent to each question.2. Do not ask any question about the contents of this examination fromanyone.a. If you think that there is something wrong with any of thequestions, attempt it to the best of your understanding.b. If you believe that some essential piece of information is missing,make an appropriate assumption and use it to solve the problem.c. Write all steps, missing steps may lead to deduction of marks.3. You are allowed to use the calculator & Statistical tables in order to solve thequestions.4. For your convenience we are providing you the following symbols,Σ or write Mean, s,σ or sd for standard ,∩, X deviation, s2 σ 2 or sd2 orvariance for variance, ,

Σlog x,for square root or whole square root.**WARNING: Please note that Virtual University takes serious note of unfairmeans. Anyone found involved in cheating will get an `F` grade in thiscourse.For Teacher's use onlyQuestion 1 2 3 4 5 6 7 8 9 TotalMarksQuestion No: 1 ( Marks: 1 ) - Please choose oneThe least squares regression line always goes through the:►Centre of the distribution►-0.5 and +0.5►Means of X and Y►

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None of the theseQuestion No: 2 ( Marks: 1 ) - Please choose oneCumulative frequency polygon is also known as:►Histogram►Pie chart►Frequency Polygon►OgiveQuestion No: 3 ( Marks: 1 ) - Please choose oneIf any value in the series is negative, the geometric mean will be:►Negative► Positive►Zero►UndefinedQuestion No: 4 ( Marks: 1 ) - Please choose oneWhen three dice are rolled then number of possible sample points is:►6►18►36►216Question No: 5 ( Marks: 1 ) - Please choose oneCorrect formula of is : 3 m►

( )/ / / / 33 2 1 1 3m − 2m m + m►

( )/ / / / 33 2 1 1 m −3m m + m►

( )/ / / / 33 2 1 1 m − 3m m + 2 m►None of the theseQuestion No: 6 ( Marks: 3 )What is five number Summary?

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Question No: 7 ( Marks: 3 )When ,find

n = 5,ΣX = 30, SX = 3.286

ΣX 2

from the given information.Question No: 8 ( Marks: 10 )During the first 10 weeks of a session, marks obtained by two students A and B were as follows.A 58 59 60 54 65 66 52 75 69 52B 56 87 80 78 72 73 84 65 66 48Which of the two students A and B was more consistent?Question No: 9 ( Marks: 9 )Show that in a single throw of two dice, the probability of throwing more than 7 is equal to that ofthrowing less than 7, and hence find the probability of exactly 7.

STA301- MCQs:


If = , = , = and =

Then find F (1)


Write down the formula of mathematical expectation.

e=(w * p) + (-v *1). e Question No: 23 ( Marks: 3 )

Discuss the statistical independence of two discrete random variables:


For given data calculate the mean and standard deviation of sampling distribution of mean if the sampling is down without replacement.

301


Elaborate the Least Significant Difference (LSD) Test.


State the Bayes’ Theorem.


The means and variances of the weekly incomes in rupees of two samples of workers are given in the following table, the samples being randomly drawn from two different factories:

Calculate the 90% confidence interval for the real difference in the incomes of the workers from the two factories.


From the given data and .

Carry out the significance test for the stated hypothesis.


Given the Probability density function.

Compute the distribution function F(x).

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a) Verify that f(x,y) is a joint density function.

b) Calculate


Let be a random sample of size 3 from a population with

mean 2and variance

Consider the following two estimators of the mean

Which estimator should be preferred?


For a particular data the value of Pearson’s coefficient of skewness is greater then zero. What will be the shape of distribution?


► J-shaped

► Symmetrical



In measures of relative dispersion unit of measurement is:

► Changed ► Vanish

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► Does not changed ► Dependent Question No: 3 ( Marks: 1 ) - Please choose one


► 0 to 1 ► 0 to -∞ ► -∞ to +∞ ► 0 to +∞ Question No: 4 ( Marks: 1 ) - Please choose one

In chi-square test of independence the degrees of freedom are:

► n - p ► n - p-1 ► n - p- 2 ► n – 2 Question No: 5 ( Marks: 1 ) - Please choose one

The Chi- Square distribution is continuous distribution ranging from:

► -∞ ≤ χ2≤ ∞ ► -∞ ≤χ2 ≤1 ► -∞ ≤χ2 ≤0 ► 0 ≤ χ2≤ ∞ 348 Question No: 6 ( Marks: 1 ) - Please choose one


►

►

►

► answr


If ŷ is the predicted value for a given x-value and b is the y-intercept then the 304

equation of a regression line for an independent variable x and a dependent variable y is:

► ŷ = mx + b, where m = slope ► x = ŷ + mb, where m = slope ► ŷ = x/m + b, where m = slope ► ŷ = x + mb, where m = slope Question No: 8 ( Marks: 1 ) - Please choose one

The location of the critical region depends upon:

► Null hypothesis ► Alternative hypothesis ► Value of alpha ► Value of test-statistic Question No: 9 ( Marks: 1 ) - Please choose one

The variance of the t-distribution is give by the formula:

►

►

►

►


Which one is the correct formula for finding desired sample size?

►

►

►

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►



► Non-negative ► Negative ► One ► Zero Question No: 12 ( Marks: 1 ) - Please choose one

E(4X + 5) =__________

► 12 E (X) ► 4 E (X) + 5 ► 16 E (X) + 5 ► 16 E (X) Question No: 13 ( Marks: 1 ) - Please choose one

How P(X + Y < 1) can be find:

► f(0, 0) + f(0, 1) + f(1, 2) ► f(2, 0) + f(0, 1) + f(1, 0) ► f(0, 0) + f(1, 1) + f(1, 0) ► f(0, 0) + f(0, 1) + f(1, 0) Question No: 14 ( Marks: 1 ) - Please choose one

The __________:

►

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►

►

►



► .0401

► .5500

► .4599 ► .9599 Question No: 16 ( Marks: 1 ) - Please choose one

In normal distribution M.D. =

► ► ► ► Question No: 17 ( Marks: 1 ) - Please choose one

In an ANOVA test there are 5 observations in each of three treatments. The degrees of freedom in the numerator and denominator respectively are....... ► 2, 4 ► 3, 15 ► 3, 12 ► 2, 12 Question No: 18 ( Marks: 1 ) - Please choose one


► Finite Set

► Infinite Set ► Universal Set

► No of these

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Stem and leaf is more informative when data is : ► Equal to 100


► Less than 100



A population that can be defined as the aggregate of all the conceivable ways in which a specified event can happen is known as:

► Infinite population ► Finite population ► Concrete population ► Hypothetical population



P (A) P (B)

P (A) + P (B)

P (A) * P (B|A)

P(B\A)*P(B)



1

1/2

1

-1/2


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1/6

2/36

1/36

1/12



0.65

0.05

0.03

0.07

Twenty percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomial distribution is:


20

2

4

16



1

0

1/2

2



309

Less than one

Greater than one


Zero

Question # 8 of 10 ( Start time: 01:38:25 PM )

Total Marks: 1

E(4X + 5) =__________


12 E (X)

4 E (X) + 5

16 E (X) + 5

16 E (X)



Mean

Variance

Mean & variance




Binomial experiment



Poisson experiment


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Mean deviation is always:

► Less than S.D ► Greater than S.D ► Greater or equal to S.D ► Less or equal to S.D Question No: 2 ( Marks: 1 ) - Please choose one

The value of χ2can never be :

► Zero ► Less than 1 ► Greater than 1 ► Negative



►

►

►

►



►

►

►

► Question No: 5 ( Marks: 1 ) - Please choose one

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Evaluate: (9-4)! ► 362880 ► 120 ► 24 ► 6 Question No: 6 ( Marks: 1 ) - Please choose one

Which formula represents the probability of the complement of event A: ► 1 + P (A) ► 1 - P (A) ► P (A) ► P (A) -1 Question No: 7 ( Marks: 1 ) - Please choose one

Ideally the width of confidence interval should be:

► 0 ► 1 ► 99 ► 100 Question No: 8 ( Marks: 1 ) - Please choose one

If the sampling distribution of is normal, the interval includes:

► 99% of the sample means

► 99.73% of the sample means




The probability distribution of a statistic is called the:

► Population distribution

► Frequency distribution ► Sampling distribution

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► Sample distribution



► E (T) =

► E (T) =T

► E (T) =0

► E (T) =1


If the following is a probability distribution, then what is the value of 'a':

X 1 2 3

P(X) 0.1 a 0.1

► 0.6 ► 0.8 ► 0.2 ► 0.4 Question No: 12 ( Marks: 1 ) - Please choose one


► Non-negative ► Negative ► One ► Zero


An expected value of a random variable is equal to:

313

► Variance ► Mean ► Standard deviation ► Covariance Question No: 14 ( Marks: 1 ) - Please choose one

The __________:

►

►

►

►



► .0401

► .5500








Which of the following is impossible in sampling:

314

► Destructive tests ► Heterogeneous ► To make voters list ► None of these Question No: 18 ( Marks: 1 ) - Please choose one

Which of the following is a systematic arrangement of data into rows and columns? ► Classification ► Tabulation ► Bar chart ► Component bar chart Question No: 19 ( Marks: 1 ) - Please choose one

Which one of the following statements is true regarding a sample? ► It is a part of population ► It must contain at least five observations ► It refers to descriptive statistics ► It produces True value Question No: 20 ( Marks: 1 ) - Please choose one

The data for an ogive is found in which distribution? ► A relative frequency distribution ► A frequency distribution ► A joint frequency distribution ► A cumulative frequency distribution

1- Hypothesis refers to The outcome of an experimentA conclusion drawn from an experimentA form of bias in which the subject tries to outguess the experimenter A tentative statement about the relationship2- Statistics is used by researchers to Analyze the empirical data collected in a studyMake their findings sound betterOperationally define their variablesEnsure the study comes out the way it was intended3- A literature review requires

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PlanningGood & clear writingLot of rewritingAll of the above 4- A literature review is based on the assumption thatCopy from the work of others Knowledge accumulates and learns from the work of othersKnowledge disaccumulatesNone of the above option

5- A theoretical frameworkElaborates the r/s among the variablesExplains the logic underlying these r/sDescribes the nature and direction of the r/sAll of the above6- Which of the following statement is not true?A research proposal is a document that presents a plan for a projectA research proposal shows that the researcher is capable of successfully conducting the proposed research projectA research proposal is an unorganized and unplanned projectA research proposal is just like a research report and written before the research project7- Preliminary data collection is a part of the Descriptive research Exploratory researchApplied research Explanatory research8- Conducting surveys is the most common method of generating Primary dataSecondary dataQualitative dataNone of the above

9- After identifying the important variables and establishing the logical reasoning in theoretical framework, the next step in the research process is To conduct surveysTo generate the hypothesisTo focus group discussionsTo use experiments in an investigation10- The appropriate analytical technique is determined by The research design

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Nature of the data collectedNature of the hypothesisBoth A & BPersonal interviews conducted in shopping malls are known as:

Mall interviewsMall intercept interviewsBrief interviewsNone of the given options

WATS lines provided by long distance telephone service at fixed rates. In this regard, WATS is the abbreviation of:

West Africa Theological SeminaryWashtenaw Area Transportation StudyWide Area Telecommunications ServiceWorld Air Transport Statistics

A list of questions which is handed over to the respondent, who reads the questions and records the answers himself is known as the:

Interview scheduleQuestionnaireInterview guideAll of the given options

One of the most critical stages in the survey research process is:

Research designQuestionnaire designInterview designSurvey design

Question that consists of two or more questions joined together is called a:

Double barreled questionGeneral questionAccurate questionConfusing question

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The number of questionnaires returned or completed divided by the total number of eligible people who were contacted or asked to participate in the survey is called the:

Response rateParticipation rateInflation rateNone of the given options

To obtain the freest opinion of the respondent, when we ask general question before a specific question then this procedure is called as the:

Research techniqueQualitative techniqueFunnel techniqueQuantitative technique

A small scale trial run of a particular component is known as:

Pilot testingPre-testingLab experimentsBoth A & B

Field testing of the questionnaire shows that:

Respondents are willing to co-operateRespondents are not willing to co-operateRespondents do not like any participationAll of the given options

Service evaluation of hotels and restaurants can be done by the:

Self-administered questionnairesOffice assistantManagerNone of the given options

The ___________analysis is a technique for gathering and analyzing the content of a text:

Content analysisGraphical analysisField analysisMathematical analysis

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__________is the strength or power of a message in a direction:

IntensityFrequencyDirectionSpace

__________data refers to information gathered by someone other than the researcher conducting the present study:

Primary dataSecondary dataQualitative dataQuantitative data

___________research produces soft data:

Qualitative researchQuantitative researchDescriptive researchApplied research

____________research produces hard data:

Qualitative researchQuantitative researchDescriptive researchApplied research

___________research is based on naturalism:

Field researchDescriptive researchBasic researchApplied research

_________interview is always with one respondent alone:

Survey interviewField interviewTelephone interviewElectronic interview

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Historiography is the method of doing _________research or of gathering & analyzing historical evidence:

Historical researchBasic researchApplied researchAction research

Historical comparative researches often use _________sources or different data types in combination:

Primary sourcesSecondary sourcesInternal sourcesExternal sources

_________is a comprehensive description and analysis of a single situation in a number of specific situations or cases:

Case studyContent analysisField researchNone of the given options

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321

1. Which one of the following sets is the measure of central tendency? Mean, standard deviation, modeMean, median, standard deviationArithmetic mean, median, modeStandard deviation, internal validity, mode

In lab experiment the effect of Variables is controlled to evaluate the causal relationship. ExtraneousModerateInterveningAll of the above

Internal validity refers to . Researcher’s degree of confidence.GeneralizabilityOperationalizationAll of the above

322

Which of the following is the weakest experimental design? One group pretest-posttest designQuasi- experimental designTwo group posttest only designEx post facto design

How many times the students appear in the research class is the example of _________. IntensitySpaceFrequencyDirection

Disadvantage of content analysis is . Researcher can increase the sample size Provides access on the subjects to which researcher does have physical access.Sometime documents provide incomplete account to the researcherSpontaneous feelings can be recorded when they occurred

7. Which of the following statement is incorrect with respect to “An experimental design is a set of procedures specifying:”How the test units (subjects) are to be divided into homogenous sub samples.What independent variables or treatments are to be measured?What dependent variables are to be measured?How the extraneous variables are to be controlled?

8. Time consumed in mall intercept interview is . HighModerateLowNil

9. “Teacher should create a friendly environment in the classroom” this is the type of . Leading questionLoaded questionDouble BarreledBurdensome question

10. Departmental stores selected to test a new merchandising display system is the example of . Quota sampling

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Convenience samplingJudgmental samplingPurposive sampling

Discrete variable is also called……….

Categorical variable Discontinuous variableBoth A & B None of the above

“Officers in my organization have higher than average level of commitment”

324


Descriptive HypothesisDirectional HypothesisRelational HypothesisAll of the above

325

‘Science’ refers to……….

A system for producing knowledge The knowledge produced by a systemBoth A & BNone of the above

Which one of the following is not a characteristic of scientific method?

DeterministicRationalismEmpiricalAbstraction

The theoretical framework discusses the interrelationships among the……….

VariablesHypothesisConceptTheory

………research is based on naturalism.

Field researchDescriptive researchBasic researchApplied research

Personal interviews conducted in shopping malls are known as………

Mall interviewsMall intercept interviewsBrief interviewsNone of the given options

……… is used to obtain the freest opinion of the respondent, by asking general question before a specific question.

Research technique

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Qualitative techniqueFunnel techniqueQuantitative technique

In, ……… the interviewer and members jointly control the pace and direction of the interview.

Field interviewTelephonic interviewBoth A and BNone of the given options

Randomization of test units is a part of ………

PretestPosttestMatchingExperiment

The independent variable is;

The variable manipulated in order to observe its effects

The variable that is measured

The free spirited variable

A confounding variableIf a researcher was studying the use of various instructional approaches to the "multiple intelligences" of his students, he is likely to be conducting which type of research?

Basic

Applied

Evaluation

Grounded theoryResearch may differ along a series of dimensions. Which of the following may be applied to this statement? The type of data collected.

The data-collection technique.

The level of manipulation used to elicit data collection.Which of the following is least likely to occur as an ethical problem with e-research?People are not likely to be able to stop once they have begun participating.

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Informed consent cannot be completely monitored.

Debriefing could be avoided.

Privacy could be invaded.

All of the given options

Which of the following is the least obtrusive and most accurate method for recording data in an interview?

Note taking

Videotaping

Audio taping

Writing notes after the interview

The most critical areas of an article to read is; Results section

Introduction

Abstract

LimitationsQuantitative social researchers rarely claim to have established causality because:

They are more concerned with publishing the results of their

reliability tests. They do not believe that this is an appropriate goal to be striving for.

They keep forgetting which of the variables they have manipulated.

They tend to use cross-sectional designs, which produce only correlations.

Which of the following is most beneficial to read in an article?

Methods

Introduction

Figures

ReferencesIf a nominal scale is used, it is permissible to calculate which of the following statistics? Mean

Range

Percentile

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ModeOne of the preoccupations of quantitative researchers is with generalization, which is a sign of: External validity

Internal reliability

External reliability

Internal validityWhich of the following is the least appropriate research problem? Does studying Latin improve the standardized vocabulary test scores of seventh grade students?

Does a drilling fifth grade student with multiplication facts improve their standardized test scores?

What is the relationship between students' math attitudes

and math achievement? Should students have access to controversial novels in school?The following journal article would be an example of _______ research; "The benefits of florescent lighting on production in a factory setting."

Applied

Interview

Basic

StupidThe purpose of a literature review is to:

Help you find out what is already known about this area.

Identify any inconsistencies or gaps in the literature.

Demonstrate an awareness of the theoretical context in which the current study can be located.

Find what is already known, identify gaps demonstrate awareness.Quantitative research has been criticized because: The measurement process suggests a spurious and artificial sense of accuracy.

The reliance on instruments and procedures makes it high in

ecological validity. It underestimates the similarities between

objects in the natural and social worlds. It has no validity.The ________ is only useful if the concepts, ideas, questions, etc. to be investigated are both testable and falsifiable.Independent Variable

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Dependent Variable

Experimental Method

Scientific MethodA ________ scale only assigns numbers to objects to classify the objects according to the characteristic of interest.

Ratio

Nominal

Interval

Dichotomous12. Which of the following true about the relationship between theory building and data collection?

When studies come out as expected, inductive support for the theory is gained.

If an experiment fails, discarding the experiment is an example of affirming the consequent.

When a hypothesis is not supported, virtually nothing has been learned about the theory.

A good theory will be inclusive enough to explain every possible research outcome.Ms. Laiba has decided to use the test at the end of the textbook to measure the achievement levels of the students in her study. Which of the following BEST describes the chapter test?

Definition Construct Variable Operationalized variableWhat is the reason for consulting handbooks, yearbooks, encyclopedias, or reviews in the initial stages of identifying a research topic?

They are readily available.

They provide an overview of the issues related to a topic.

They are primary sources.

They avoid reporting statistical data so one can interpret the results more easily.What type of process research is?A process to discover the truth

A process to invent the machines

A process to make new medicines

A process to create theoriesWhich one of the following is not an assumption of science?

There are reoccurring patterns in the world.

330

Events happen because of preceding causes.

We can discover solutions to problems of interest.

Theoretical explanations must agree with common sense.

A good qualitative problem statement: Defines the independent and dependent variables

Conveys a sense of emerging design

Specifies a research hypothesis to be tested

Specifies the relationship between variables that the researcher expects to find.

Why do you need to review the existing literature?

, To give your dissertation a proper academic appearance, with lots of references

, Because without it, you could never reach the required word-count

, To find out what is already known about your area of interest

, To help in your general studying

If a researcher was studying the use of various instructional approaches to the "multiple intelligences" of his students, he is likely to be conducting which type of research?

Basic

Applied

Evaluation

Grounded theory

Ms. Roshi has been coordinating the Annual Festival at her school for the last several years. She wants to be sure the students and parents enjoy the festival again this year. On which source is she LEAST likely to rely when making decisions about what to do?Select correct option:

Tradition

331

Personal experience

Research

Expert opinion

A review that only demonstrates familiarity with an area is rarely published but it often is part of an educational program is which type of review?

Integrative reviews

Theoretical reviews

Self-study reviews

Historical reviews

A researcher developed a measure of shyness and is now asking whether this measure does in fact measure a person's true state of shyness. This is a question of:

Reactivity

Construct validity

Reliability

Content validity

When you are confident that the experimental manipulation produced the changes you measured in the dependent variable, your study probably has good ________ validity.

Construct

Internal

External

Causal

If a researcher is studying the effect of using laptops in his classroom to ascertain their merit and worth, he is likely conducting which type of research?Select correct option:

Basic

332

Applied

Evaluation

Experimental

When doing research involving deception with human subjects, researchers have an obligation to do which of the following?

Tell subjects the truth about the study’s purpose and methods after the study is completed

Prevent mental and physical harm to subjects

Let subjects withdraw from the study at any time if they don’t want to keep participating

All of the given options

A literature review requires;

planning

clear writing

good writing

All of the given option

A measure has high internal consistency reliability when:

Multiple observers make the same ratings using the measure.

Participants score at the high end of the scale every time they complete the measure.

Multiple observers obtain the same score every time they use the measure.

Each of the items correlates with other items on the measure.

Which of the following is not a function of clearly identified research questions?

They guide your literature search.

They keep you focused throughout the data collection period.

They make the scope of your research as wide as possible.

They are linked together to help you construct a coherent

333

argument.

Procedures determining what two issues are rarely used in quantitative research?

Objectivity and subjectivity

Reliability and validity

Accessibility and replicability

Quality and quantity

Which of the following true about the relationship between theory building and data collection?

When studies come out as expected, inductive support for the theory is gained.

If an experiment fails, discarding the experiment is an example of affirming the consequent.

When a hypothesis is not supported, virtually nothing has been learned about the theory.

A good theory will be inclusive enough to explain every possible research outcome.

Temperature is measured from which scale?NominalOrdinalIntervalAll the given options.

Which of the following is a threat to internal validity of an experimental design?MaturationInteraction of setting and treatmentInteraction effects of pre-testingreactive effects of experimental designWhich of the following statements is correct about validity and reliability?When internal validity is high, external validity is lowWhen internal validity is high, there is no change in external validityWhen internal validity is high, external validity is also highAll of the given option

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Which of the following effect in internal validity occurs when test units with extreme scores move closer to the average score during the course of the experiment?Statistical Regression Selection biasMaturationInstrumentation

Interval scale measures which of the following?The distance between each participant’s individual scoreAn individual’s score from zero upwardsmore or less of some underlying assumptionsAbsolute Zero

Which of the following best describes an assessment that examines students ability to conduct a chemistry experiment in the lab?Aptitudeinterest inventoryPerformance AssessmentStandardized test

Which of the following are legitimate frameworks for setting out a literature review?(1)Constructing interextual coherence (2) Deconstruction of textual coherence(3) Problematizing the situation (4) Resolving the discovered problems?

1 &22&31&32&4

If researcher was studying the use of various instructional approaches to the “multiple intelligence” of his students, he is likely to be conducting which of the following type of research?BasicEvaluationAppliedGround theory

Which of the following is most beneficial to read in an article?MethodsIntroductionFiguresreference

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One of the preoccupations of quantitative researchers is with generalization, which is a sign ofExternal validityInternal ReliabilityExternal ReliabilityInternal validity

Which of the following is likely to reduce the validity of a test?Unclear test directionsAmbiguous test itemsUnclear, ambiguous and untaught itemsUntaught items

1. Question # 1 of 10 ( Start time: 08:23:14 PM ) Total Marks: 1

If Y=bX, then variance of Y isSelect correct option: b*2 var(x) var(x) b var(x) b square root var(x)

2. Question # 2 of 10 ( Start time: 08:24:38 PM ) Total Marks: 1If f(x) is a continuous probability function, then P(X = 2) is:Select correct option: 1 0 1/2 2 3. Question # 3 of 10 ( Start time: 08:25:52 PM ) Total Marks: 1In regression line Y=a+bX, Y is called:Select correct option: Dependent variable Independent variable Explanatory variable Regressor

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4. Question # 4 of 10 ( Start time: 08:26:51 PM ) Total Marks: 1If A and B are mutually exclusive events with P (A) =0.25 and P (B) = 0.50, Then P (A or B) =………Select correct option: 0.25 0.75 0.50 1 5. Question # 5 of 10 ( Start time: 08:28:06 PM ) Total Marks: 1Symbolically, a conditional probability is:Select correct option: P(AB) P(A/B) P(A) P(AUB) 6. Question # 6 of 10 ( Start time: 08:28:42 PM ) Total Marks: 1In a 52 well shuffled pack of 52 playing cards, the probability of drawing any one diamond card isSelect correct option: 1/52 4/52 13/52 52/52 7. Question # 7 of 10 ( Start time: 08:30:13 PM ) Total Marks: 1Probability of a sure event isSelect correct option: 8 1 0 0.5

8. Question # 8 of 10 ( Start time: 08:31:42 PM ) Total Marks: 1If Y=3X+5,then S.D of Y is equal toSelect correct option: 9 s.d(x) 3 s.d(x) s.d(x)+5 3s.d(x)+59. Question # 9 of 10 ( Start time: 08:33:16 PM ) Total Marks: 1The probability of drawing a red queen card from well-shuffled pack of 52 playing cards isSelect correct option: 4/52

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2/52 13/52 26/5210. Question # 10 of 10 ( Start time: 08:34:40 PM ) Total Marks: 1If P (B|A) = 0.25 and P (A and B) =0.20, then P (A) isSelect correct option: 0.05 0.80 0.95 0.7511. Question # 1 of 10 ( Start time: 08:57:45 PM ) Total Marks: 1When a coin is tossed 3 times, the probability of getting 3 tails isSelect correct option: 1/8 3/8 3/6 2/812. Question # 2 of 10 ( Start time: 08:59:14 PM ) Total Marks: 1In how many ways can a team of 11 players be chosen from a total of 16 players?Select correct option: 4368(not confirmed) 2426 5400 268013. Question # 3 of 10 ( Start time: 09:00:38 PM ) Total Marks: 1The standard deviation of c (constant) isSelect correct option: c c square 0 does not exist14. Question # 4 of 10 ( Start time: 09:01:46 PM ) Total Marks: 1If P (E) is the probability that an event will occur, which of the following must be false:Select correct option: P(E)= - 1 P(E)=1 P(E)=1/2 P(E)=1/315. Question # 5 of 10 ( Start time: 09:02:48 PM ) Total Marks: 1Let E and F be events associated with the same experiment. Suppose the E and F are independent and that P(E) = 1/4 and P(F) = 1/2 Then P(E U F) is:Select correct option: 1/8 3/4 7/8 5/8

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16. Question # 6 of 10 ( Start time: 09:04:09 PM ) Total Marks: 1A student solved 25 questions from first 50 questions of a book to be solved. The probability that he will solve the remaining all questions is:Select correct option: 0.25 0.5 1 0 17. Question # 7 of 10 ( Start time: 09:05:31 PM ) Total Marks: 1If Y=bX, then variance of Y isSelect correct option: b*2 var(x) var(x) b var(x) b square root var(x) 18. Question # 9 of 10 ( Start time: 09:07:48 PM ) Total Marks: 1The classical definition of probability assumes:Select correct option: Exhaustive events Mutually exclusive events Equally likely evens Independent evens 19. Question # 10 of 10 ( Start time: 09:08:50 PM ) Total Marks: 1In scatter diagram, the variable plotted along Y-axis is:Select correct option: Independent variable Dependent variable Continuous variable Discrete variable 20. Which of the following measures of dispersion are based on deviations from the mean? Select correct option:

Variance Standard deviation Mean deviation

All of the these 21. What does it mean when a data set has a standard deviation equal to zero?


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All values of the data appear with the same frequency. The mean of the data is also zero. All of the data have the same value. There are no data to begin with. 22. A set of possible values that a random variable can assume and their associated probabilities of occurrence are referred to as ________. Select correct option:

Probability distribution The expected return The standard deviation Coefficient of variation 23. Which of the following can never be probability of an event? Select correct option:

0 1 0.5 -0.5 24. The standard deviation of -1, -1, -1, -1 will be Select correct option:

1 -1 0 Does not exist 25. Which formula represents the probability of the complement of event A: Select correct option:

1 + P (A) 1 - P (A) P (A) P (A) -1 26. The Special Rule of Addition is used to combine: Select correct option:

Independent Events Mutually Exclusive Events Events that total more than 1.00 Events based on subjective probabilities

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27. set which is the sub-set of every set is Select correct option:

Empty Set Power Set Universal Set Super Set 28. E(4X + 5) =________ Select correct option:

12 E (X) 4 E (X) + 5 16 E (X) + 5 16 E (X) 29. When two dice are rolled the number of possible sample points is : Select correct option:

6 12 24 36 30. Question # 1 of 10 ( Start time: 09:43:04 PM ) Total Marks: 1 If two events A and B are not mutually exclusive then Select correct option:

P (A or B) = P (A) + P (B) – P (A and B)

P (A or B) = P (A) + P (B)

P (A or B) = P (A) x P (B)

P (A or B) = P (A) + P (B) 31.

Question # 2 of 10 ( Start time: 09:43:59 PM ) Total Marks: 1 Evaluate (10-4)! Select correct option:

1000 720 480 32 32. Question # 3 of 10 ( Start time: 09:45:01 PM ) Total Marks: 1 When E is an impossible event, then P(E) is:

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0 1 2 0.5 33. Question # 4 of 10 ( Start time: 09:46:20 PM ) Total Marks: 1 When we toss a coin , we get only: Select correct option:

1 outcome 2 outcome 3 outcome 4 outcome 34.

Question # 5 of 10 ( Start time: 09:47:15 PM ) Total Marks: 1 For exhaustive events, the P(AUBUC) is equal to: Select correct option:

P(A) P(S) P(A) * P(B)* P(C) P(B) 35. Question # 6 of 10 ( Start time: 09:48:21 PM ) Total Marks: 1 A student solved 25 questions from first 50 questions of a book to be solved. The probability that he will solve the remaining all questions is: Select correct option:

0.25 0.5 1 0 36. A set of possible values that a random variable can assume and their associated probabilities of occurrence are referred to as ________. Select correct option:

Probability distribution The expected return The standard deviation Coefficient of variation 37.

Question # 9 of 10 ( Start time: 09:50:35 PM ) Total Marks: 1 If we roll a die then probability of getting a ‘6’ will be

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2/6

1/6

4/6

1 38. Question # 10 of 10 ( Start time: 09:51:36 PM ) Total Marks: 1 If P(A) = 0.45, P(B) = 0.35, and P(A and B) = 0.25, then P(A | B) is: Select correct option:

1.4 1.8 0.714 0.556 39. Question # 8 of 10 ( Start time: 09:49:53 PM ) Total Marks: 1 Which of the following is not a measure of central tendency? Select correct option:

Percentile

Quartile

Standard deviation

Mode 40. Question # 1 of 10 ( Start time: 09:56:49 PM ) Total Marks: 1 Random experiment can be repeated any no. of times under the……… conditions. Select correct option:

Different Similar

41. Question # 2 of 10 ( Start time: 09:58:09 PM ) Total Marks: 1 What is the probability of sure event? Select correct option:

0 1 0.5 2

42. Question # 3 of 10 ( Start time: 09:58:41 PM ) Total Marks: 1 The simultaneous occurrence of two events is called:

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Joint probability Subjective probability Prior probability Conditional probability43. Question # 4 of 10 ( Start time: 09:59:47 PM ) Total Marks: 1 In regression analysis, the variable that is being predicted is the Select correct option:

Dependent variable

Independent variable

Intervening variable

None of these

6. Question # 1 of 10 ( Start time: 08:23:14 PM ) Total Marks: 1If Y=bX, then variance of Y isSelect correct option: b*2 var(x) var(x) b var(x) b square root var(x)

7. Question # 2 of 10 ( Start time: 08:24:38 PM ) Total Marks: 1If f(x) is a continuous probability function, then P(X = 2) is:Select correct option: 1 0 1/2 2

8. Question # 3 of 10 ( Start time: 08:25:52 PM ) Total Marks: 1In regression line Y=a+bX, Y is called:Select correct option: Dependent variable Independent variable Explanatory variable Regressor

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9. Question # 4 of 10 ( Start time: 08:26:51 PM ) Total Marks: 1If A and B are mutually exclusive events with P (A) =0.25 and P (B) = 0.50, Then P (A or B) =………Select correct option: 0.25 0.75 0.50 1

10. Question # 5 of 10 ( Start time: 08:28:06 PM ) Total Marks: 1Symbolically, a conditional probability is:Select correct option: P(AB) P(A/B) P(A) P(AUB)

11. Question # 6 of 10 ( Start time: 08:28:42 PM ) Total Marks: 1In a 52 well shuffled pack of 52 playing cards, the probability of drawing any one diamond card isSelect correct option: 1/52 4/52 13/52 52/52

12. Question # 7 of 10 ( Start time: 08:30:13 PM ) Total Marks: 1Probability of a sure event isSelect correct option: 8 1 0 0.5

13. Question # 8 of 10 ( Start time: 08:31:42 PM ) Total Marks: 1If Y=3X+5,then S.D of Y is equal toSelect correct option:

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9 s.d(x) 3 s.d(x) s.d(x)+5 3s.d(x)+5

14. Question # 9 of 10 ( Start time: 08:33:16 PM ) Total Marks: 1The probability of drawing a red queen card from well-shuffled pack of 52 playing cards isSelect correct option: 4/52 2/52 13/52 26/52

15. Question # 10 of 10 ( Start time: 08:34:40 PM ) Total Marks: 1If P (B|A) = 0.25 and P (A and B) =0.20, then P (A) isSelect correct option: 0.05 0.80 0.95 0.75

16. Question # 1 of 10 ( Start time: 08:57:45 PM ) Total Marks: 1When a coin is tossed 3 times, the probability of getting 3 tails isSelect correct option: 1/8 3/8 3/6 2/8

17. Question # 2 of 10 ( Start time: 08:59:14 PM ) Total Marks: 1In how many ways can a team of 11 players be chosen from a total of 16 players?Select correct option: 4368(not confirmed) 2426 5400 2680

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18. Question # 3 of 10 ( Start time: 09:00:38 PM ) Total Marks: 1The standard deviation of c (constant) isSelect correct option: c c square 0 does not exist

19. Question # 4 of 10 ( Start time: 09:01:46 PM ) Total Marks: 1If P (E) is the probability that an event will occur, which of the following must be false:Select correct option: P(E)= - 1 P(E)=1 P(E)=1/2 P(E)=1/3

20. Question # 5 of 10 ( Start time: 09:02:48 PM ) Total Marks: 1Let E and F be events associated with the same experiment. Suppose the E and F are independent and that P(E) = 1/4 and P(F) = 1/2 Then P(E U F) is:Select correct option: 1/8 3/4 7/8 5/8

21. Question # 6 of 10 ( Start time: 09:04:09 PM ) Total Marks: 1A student solved 25 questions from first 50 questions of a book to be solved. The probability that he will solve the remaining all questions is:Select correct option: 0.25 0.5 1 0

22. Question # 7 of 10 ( Start time: 09:05:31 PM ) Total Marks: 1If Y=bX, then variance of Y is

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Select correct option: b*2 var(x) var(x) b var(x) b square root var(x)

23. Question # 9 of 10 ( Start time: 09:07:48 PM ) Total Marks: 1The classical definition of probability assumes:Select correct option: Exhaustive events Mutually exclusive events Equally likely evens Independent evens

24. Question # 10 of 10 ( Start time: 09:08:50 PM ) Total Marks: 1In scatter diagram, the variable plotted along Y-axis is:Select correct option: Independent variable Dependent variable Continuous variable Discrete variable

25. Which of the following measures of dispersion are based on deviations from the mean? Select correct option:


All of the these

26. What does it mean when a data set has a standard deviation equal to zero? Select correct option:

All values of the data appear with the same frequency. The mean of the data is also zero. All of the data have the same value. There are no data to begin with.

348

27. A set of possible values that a random variable can assume and their associated probabilities of occurrence are referred to as ________. Select correct option:

Probability distribution The expected return The standard deviation Coefficient of variation

28. Which of the following can never be probability of an event? Select correct option:

0 1 0.5 -0.5

29. The standard deviation of -1, -1, -1, -1 will be Select correct option:

1 -1 0 Does not exist

30. Which formula represents the probability of the complement of event A: Select correct option:

1 + P (A) 1 - P (A) P (A) P (A) -1

31. The Special Rule of Addition is used to combine: Select correct option:


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Empty Set Power Set Universal Set Super Set

33. E(4X + 5) =________ Select correct option:

12 E (X) 4 E (X) + 5 16 E (X) + 5 16 E (X)

34. When two dice are rolled the number of possible sample points is : Select correct option:

6 12 24 36

35. Question # 1 of 10 ( Start time: 09:43:04 PM ) Total Marks: 1 If two events A and B are not mutually exclusive then Select correct option:


P (A or B) = P (A) + P (B)

P (A or B) = P (A) x P (B)

P (A or B) = P (A) + P (B)

36.Question # 2 of 10 ( Start time: 09:43:59 PM ) Total Marks: 1 Evaluate (10-4)! Select correct option:

1000 720

350

480 32

37. Question # 3 of 10 ( Start time: 09:45:01 PM ) Total Marks: 1 When E is an impossible event, then P(E) is: Select correct option:

0 1 2 0.5

38. Question # 4 of 10 ( Start time: 09:46:20 PM ) Total Marks: 1 When we toss a coin , we get only: Select correct option:

1 outcome 2 outcome 3 outcome 4 outcome

39.Question # 5 of 10 ( Start time: 09:47:15 PM ) Total Marks: 1 For exhaustive events, the P(AUBUC) is equal to: Select correct option:

P(A) P(S) P(A) * P(B)* P(C) P(B)

40. Question # 6 of 10 ( Start time: 09:48:21 PM ) Total Marks: 1 A student solved 25 questions from first 50 questions of a book to be solved. The probability that he will solve the remaining all questions is: Select correct option:

0.25 0.5 1 0

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42.Question # 9 of 10 ( Start time: 09:50:35 PM ) Total Marks: 1 If we roll a die then probability of getting a ‘6’ will be Select correct option:

2/6

1/6

4/6

1

43. Question # 10 of 10 ( Start time: 09:51:36 PM ) Total Marks: 1 If P(A) = 0.45, P(B) = 0.35, and P(A and B) = 0.25, then P(A | B) is: Select correct option:

1.4 1.8 0.714 0.556

44. Question # 8 of 10 ( Start time: 09:49:53 PM ) Total Marks: 1 Which of the following is not a measure of central tendency? Select correct option:

Percentile

Quartile

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Standard deviation

Mode

45. Question # 1 of 10 ( Start time: 09:56:49 PM ) Total Marks: 1 Random experiment can be repeated any no. of times under the……… conditions. Select correct option:

Different Similar

46. Question # 2 of 10 ( Start time: 09:58:09 PM ) Total Marks: 1 What is the probability of sure event? Select correct option:

0 1 0.5 2

47. Question # 3 of 10 ( Start time: 09:58:41 PM ) Total Marks: 1 The simultaneous occurrence of two events is called: Select correct option:

Joint probability Subjective probability Prior probability Conditional probability

48. Question # 4 of 10 ( Start time: 09:59:47 PM ) Total Marks: 1 In regression analysis, the variable that is being predicted is the Select correct option:

Dependent variable


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None of these

Thanks to Armaan Makhani for His Sharing

1. A quantity obtained by applying certain rule or formula is known asSelect correct option:EstimateEstimator2. Criteria to check a point estimator to be good involvesSelect correct option:ConsistencyUnbiasednessEfficiencyAbove all pg 2583. The F-distribution always ranges from:Select correct option:0 to 10 to -8-8 to +80 to +84. 1-a is the probability of ......Select correct option:Type 1 errorRejection regionAcceptance regionType 2 error5. Parameter is a ………quantity.Select correct option:ConstantVariable6. To find the estimate of a parameter …….methods are used.Select correct option:TwoThreeFourMany7. A failing student is passed by an examiner. It is an example of:Select correct option:Type I errorType II errorCorrect decisionNo information regarding student exams8. For two mutually exclusive events A and B, P (A) = 0.2 and P (B) = 0.4, then P(AUB) is:Select correct option:

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0.80.20.60.5P(AUB)=P(A)+p(B)=0.2+0.4=0.69. An urn contains 4 red balls and 6 green balls. A sample of 4 balls is selected from the urnwithout replacement. It is the example of:Select correct option:Binomial distributionHypergrometric distributionPoisson distributionExponential distribution10. A standard deck of 52 cards is shuffled. What is the probability of choosing the 5 of diamonds:Select correct option:1/51/135/521/5211. If P(AnB) = 0.12 P (A) = 0.3, find P (B) where ‘A’ and ‘B’ are independent:Select correct option:0.10.20.30.40.3X0.4=0.1212. The mean deviation of the normal distribution is approximately:Select correct option:7/8 of the S.D4/5 of the S.D3/4 of the S.D1/2 of the S.D13. We use the Poisson approximation to the binomial when:Select correct option:p is 0.01 or less & n is 10 or morep is 0.05 or less & n is 20 or more pg221p is 0.04 or less & n is 15 or morep is 0.02 or less & n is 10 or more14. The conditional probability P (A\B) is:Select correct option:P(A n B)/P(B) pg157P(A n B)/P(A)P(A U B)/P(B)P(A U B)/P(A)15. We use the General Rule of Multiplication to combine:Select correct option:

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Events those are not independentMutually exclusive eventsEvents that total more than 1.00Events based on subjective probabilities16. Which statement is NOT CORRECT?Select correct option:The sample standard deviation measures variability of our sample valuesA larger sample will give answers that vary less from the true value than smaller samplesThe sampling distribution describes how our estimate (answer) will vary if a new sample is takenA large sample size always gives unbiased estimators regardless of how the sample is chosen17. Probability of an impossible event is always:Select correct option:Less than oneGreater than oneBetween one and zeroZero18. The number of parameters in uniform distribution is (are):Select correct option:12 pg 2243419. The probability can never be:Select correct option:11/21-1/220. The conditional probability P (A\B) is:Select correct option:P(A n B)/P(B)P(A n B)/P(A)P(A U B)/P(B)P(A U B)/P(A)21. A random sample of n=25 values gives sample mean 83. Can this sample be regarded as drawnfrom a normal population with µ= 80 and s= 7? In this question the alternative hypothesis willbe:Select correct option:H1: µ = 80H1: µ ? 80H1: µ > 80

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H1: µ <80 pg 27822. If f(x) is a continuous probability function, then P(X = 2) is:Select correct option:101/2223. The binomial distribution is negatively skewed when:Select correct option:p>q pg 214p<qp=qp=q=1/224. If we roll three fair dices then the total number of outcomes is:Select correct option:63621612966^3=21625. When we draw the sample with replacement, the probability distribution to be used is:Select correct option:BinomialHypergeometricBinomial & hypergeometric pg 219Poisson26. The moment ratios of normal distribution come out to be:Select correct option:0 and 10 and 20 and 3 pg 2260 and 427. The probability of an event is always:Select correct option:greater than 0less than 1between o and 1greater than 128. Symbolically, a conditional probability is:Select correct option:P(AB)P(A/B)P(A)P(AUB)29. Suppose the test scores of 600 students are normally distributed with a mean of 76 and

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standard deviation of 8. The number of students scoring between 70 and 82 is:Select correct option:27216426032830. If P (A) = 0.3 and P (B) = 0.5, find P (A/B) where ‘A’ and ‘B’ are independent:Select correct option:0.30.50.80.1531. An urn contains 4 red balls and 6 green balls. A sample of 4 balls is selected from the urnwithout replacement. It is the example of:Select correct option:Binomial distributionHypergrometric distributionPoisson distributionExponential distribution32. If the second moment ratio is less than 3 the distribution will be:Select correct option:MesokurticLeptokurticPlatykurtic pg 226None of these33. For the independent events A and B if P (A) = 0.25, P (B) =0.40 then P (A and B) =……Select correct option:0.650.10.500.15P(A)*P(B)0.25*0.40=0.134. A set of possible values that a random variable can assume and their associated probabilities ofoccurrence are referred to as __________.Select correct option:Probability distributionThe expected returnThe standard deviationCoefficient of variation35. A random variable X has a probability distribution as follows: X | 0 1 2 3 P(X) | 2k 3k 13k 2kWhat is the possible value of k:Select correct option:0.01

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0.030.050.0736. The probability of drawing any one spade card is:Select correct option:1/524/5213/5252/5237. The function abbreviated to d.f. is also called the......Select correct option:Probability density functionProbability distribution function pg 172Commutative distribution functionDiscrete function38. Binomial distribution is skewed to the right if:Select correct option:p=qP<qp>qp=n39. A discrete probability function f(x) is always:Select correct option:ZeroOne pg 172NegativeNon-negative40. For a binomial distribution, n= 10 & q= 0.6, the mean of the distribution is:Select correct option:0.66.0104P=1-q1-0.6=0.4,mean =np10*0.4=441. In the FA examination, 24candidates offered Statistics. If the probability of passing the subjectbe 1/3, what will be the mean of the distribution?Select correct option:786542. The probability that a certain machine will produce a defective item is 1/4. If a random sample

359

of 6 items is taken from the output of this machine, what is the probability that there will be 5or more defectives in the sample?Select correct option:3/409618/409619/40964/409643. Probability of type II error isSelect correct option:aB pg 2761-a1-B44. If the values of variables are increasing or decreasing in the same direction then such kind ofcorrelation is referred asSelect correct option:Zero CorrelationPerfect CorrelationPositive CorrelationNegative Correlation45. The moving averages of the Prices 55,60,65,70 areSelect correct option:70, 7560, 6565,6570,6046. The best measure of variation isSelect correct option:RangeQuartile deviationVarianceCoefficient of variance47. Ms. Christian calculated a correlation coefficient of .75. Which of the following reflects thebest interpretation of this?Select correct option:Weak negative.Strong negative.Weak positive.Strong positive.48. ………use the division of a circle into different sectors. Select correct option:Line graphSector graphsFrequency PolygonConversion Graphs

360

49. The measurement of measure of degree of to which any two variables vary together is calledSelect correct option:Regression CoefficientCorrelationBoth (a) and (b)None of these50. Analysis of Variance (ANOVA) is a test for equality of:Select correct option:variancesmeansproportionsonly two parameters51. For some data you are given Maximum value = 96 , Minimum Value = 23 , Range = 73,number of classes selected between 5 and 15 Then class width will be Select correct option:1585All options 1,2 ,3 are possible52. If strength of the association between X and Y is very weak, then r = ? Select correct option:r = - 1r = 0r = 1r = 253. The moving averages of the Prices 90,70,30,110 are Select correct option:63.33, 7073.33, 8045.45, 6865.50, 7554. With increase in sample size, distribution tends to be a.......Select correct option:Meso kurticNormalBell shapedAbove all55. In the central tendency Mean, Median and ModeSelect correct option:Mean is better than MedianMedian is better than ModeMean is better than ModeAll of these are true56. The degree to which numerical data tend to spread about an average is calledSelect correct option:The dispersion

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Standard deviationCorrelationNone of these57. …………..graphs are similar to bar graphs.Select correct option:columnlineconversionsector58. A pattern of variation of a time series that repeats every year is called:Select correct option:CyclicalSeasonalTrendSecular59. In the central tendency Mean, Median and ModeSelect correct option:Mean is better than MedianMedian is better than ModeMean is better than ModeAll of these are true60. The degree to which numerical data tend to spread about an average is calledSelect correct option:The dispersionStandard deviationCorrelationNone of these61. …………..graphs are similar to bar graphs.Select correct option:columnlineconversionsector62. A pattern of variation of a time series that repeats every year is called:Select correct option:CyclicalSeasonalTrendSecular63. You have measured the systolic blood pressure of a random sample of 22 employees of acompany. A 95% con?dence interval for the mean systolic blood pressure for the employees iscomputed to be (120,138). Which of the following statements gives a valid interpretation of thisinterval?Select correct option:

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About 95% of the sample of employees has a systoliAbout 95% of the employees in the company have aIf the sampling procedure were repeated many timesIf the sampling procedure were repeated many times64. Assume that a population consists of 7 similar containers having the following weights (km):9.8, 10.2, 10.4, 9.8, 10.0, 10.2, 9.6 What is the second moment about mean?Select correct option:0.262 kg0.069kg0.521 kg0.313kg65. How many numbers of parameter(s) are in t-distribution?Select correct option:01 pg 2922366. With increase in sample size, distribution tends to be a.......Select correct option:Meso kurticNormalBell shapedAbove all67. F-distribution is a…………….. distribution.Select correct option:Unimodel pg 312BimodalDiscreteNegatively skewed68. Which one of the following sampling methods would give unbiased results, if you need to findout the number of people in your town liking vanilla or chocolate ice creams?Select correct option:Ask my neighborsRandomly select a few ice cream shops in town, andAsk my friendsAsk my classmates69. A standard deviation obtained from sampling distribution of sample statistics is known asSelect correct option:Sampling ErrorStandard error pg 24070. If the regression line: Y= 3+5X meets y-axis at ‘8’ units distance from origin then the value ofx-intercept isSelect correct option:

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-(3/5)3/511/5171. Sum of three terms whose mean is equal to 90 isSelect correct option:27030Also 90None of these270/3=9072. FREQUENCY Function calculates how often values occur within a range of values.Select correct option:trueFalse73. Which of the following correlation coefficients represents the weakest correlation between twovariables?Select correct option:0.15-0.150.02-1.0074. If the value of r is 0.8 ,then the coefficient of determination isSelect correct option:67%64%80%75%75. If the dependent variable increases with the independent variable then the coefficient ofcorrelation isSelect correct option:0 to -10 to – 0.50 to -20 to 176. F- distribution tends to normality, ifSelect correct option:V1~8V2~8V1 and V2 ~8Sample size is large77. Consistency of an estimator can be checked by comparingSelect correct option:MeanMSE

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VarianceStandard deviation78. A standardized estimate has mean and varianceSelect correct option:(1, 0)(0, 1)(µ, s2)(µ, s)79. A composite hypothesis comprises of ………Select correct option:EqualityNot equal toLess than/greater(b) and (c)80. For a particular hypothesis test, a=0.05and B=0.05. The power of test is equal to:Select correct option:0.140.900.950.2581. In a t-distributionSelect correct option:Mean=median=modeMean>Median<ModeMedian >Mean>ModeMedia<Mode<Mean82. If we reject the null hypothesis, we might be makingSelect correct option:Type I errorType II errorA correct decisionUnpredictable83. The Central Limit Theorem is important in Statistics because it allows us to use the normaldistribution to make inferences concerning the population mean:Select correct option:Provided that the population is normally distributed aProvided that the population is normally distributed (Provided that the sample size is reasonably large (foProvided that the population is normally distributed and the population variance is known (forany sample size)84. Herbicide A has been used for years in order to kill a particular type of weed, but anexperiment is tobe conducted in order to see whether a new herbicide, Herbicide B, is more effective than

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Herbicide A.Herbicide A will continue to be used unless there is sufficient evidence that Herbicide B is moreeffective.The alternative hypothesis in this problem is thatSelect correct option:Herbicide A is more effective than Herbicide BHerbicide B is more effective than Herbicide AHerbicide A is not more effective than Herbicide BHerbicide B is not more effective than Herbicide A85. A data in which we study about Regions is called ……Select correct option:QualitativeQuantitativeGeographicalChronological86. If the median of an arrangement of numbers is equal to the mean of its middle terms then thearrangement containsSelect correct option:Odd number of termsEven number of termsUnlimited number of termsPrime number87. If the graph is very much scattered, then what can be the suitable value of r?Select correct option:r = - 0.9r = -0.5r = 0.1r=0.888. In scatter diagram, clustering of points around a straight line indicatesSelect correct option:Linear regressionNon-linear regressionCurvilinear linear regressionBoth a and b89. If the standard deviation of a population is 9, the population variance isSelect correct option:3921.358190. How many steps are involved in general procedure for testing hypothesis:4567

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91. When testing for independence in a contingency table with 2 rows and 5 columns, there are________ degrees of freedom.41075r-1*c-12-1*5-1=492. The critical region is in:The middle of a distributionThe tails of a distributionEither the middle or the tails of a distributionNeither the middle nor the tails of a distribution93. t-distribution is used to test the hypothesis about.....MeanproportionThe term 1-B is calledLevel of the testpower of the testSize of the testCritical region94. The asymptotic distribution of t-statistic with n-degree of freedom isFNormalZ T95. The Gallup Poll has decided to increase the size of its random sample of Canadian voters fromabout 1200 people to about 4000 people. The e?ect of this increase is to:Reduce the bias of the estimateIncrease the standard error of the estimateReduce the variability of the estimateIncrease the con?dence interval width for the parameter96. The value of chi square can never be :ZeroLess then 1Greater then 1Negative97. The curve of the F- distribution depends upon:MeanVarianceStandard DeviationSample Size98. We want to test H0 : µ = 1.5 vs. H1 : µ 6= 1.5 at _= .05 . A 95% confidence interval for µcalculated from a given random sample is (1.4, 3.6)Based on this finding we:Fail to reject H0

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Reject H0Cannot make any decision at all because the value of the test statistic is not availableCannot make any decision at all because (1.4, 3.6) is only a 95%99. When we want to test the equality of two variances we usually useF-testChi-square testANOVAZ_test100. To find the estimate of a parameter …….methods are used.TwoThreeFourMany101. In testing hypothesis, we always begin it with assuming that:Null hypothesis is trueAlternative hypothesis is trueSample size is largePopulation is normal102. t-distribtion is applicable in case ofIndependent samplesDependent samplesBoth (a) and (b)Normal populations103. When testing for independence in a contingency table with 3 rows and 4 columns, there are________ degrees of freedom.56712104. The Chi- Square distribution is continuous distribution ranging from:0 = ?2= 8-8 =?2 =0-8 =?2 =1-8 = ?2= 8105. The location of the critical region depends upon:Null hypothesisAlternative hypothesisValue of alphaValue of test-statistic106. A random sample of n = 6 has the elements 6, 10,13,14,18 and 20. What is the pointestimate of the population mean?1213.51111.5

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107. ML estimators may not ………ConsistentEfficientUnbiasedBised108. Which of the following reveals the weakest fact.Select correct option:The measure of central tendency measures that value which depends only on the extreme valuesThe measure of central tendency measures that value in tha data which occurs in the data most frequenttimes.The measure of central tendency measures the value which has tendency to lie in the central part of thedata.109. The measure of central tendency measures the distance of values from meansFrequency polygon is …………Select correct option:Bar ChartsA line graphPareto ChatsNone of these110. A bar graph uses ……to show data.Select correct option:PointsBarsLinesPictures111. Geographical data deals with…Select correct option:ReligionHeightIncomeRegions112. Which one provides the basis for hypothesis testing?Null hypothesisAlternative hypothesisCritical valueTest-statistics113. The test statistic to test the U1 = U2 (U represent the mean of population)for normalpopulation for n>30.F-testZ-testT-testChi-Square test114. In a t-distribution

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Mean=median=modeMean>Median<ModeMedian >Mean>ModeMedia<Mode<Mean115. 1-a is the probability of ......Type 1 errorRejection regionAcceptance regionType 2 error116. Inferential statistics involves …….TestingConfidence intervalEstimationAbove all117. Probability of type II error isaB1-a1-B118. if the equation of regression line is y = 5, then what result will you take out from it?Select correct option:The line passes through origin.The line passes through (5, 0)The line is parallel to y-axis.The line is parallel to x-axis.119. If the estimating equation is Y = a – b X ,Which of the following is trueSelect correct option:a)The y intercept is’b’b) Slope of line is negativec) There is inverse relationshipd) b & c120. The variance of t-distribution, for v >2, is always:Select correct option:Greater than zeroLess than oneEqual to oneGreater than one121. Alpha is the probability of ......Select correct option:Rejecting H0Accepting H0Rejecting H1Accepting H1122. What type of data is collected in population census?Select correct option:Two Types

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123. The collection of all outcomes for an experiment is calledSelect correct option:a sample spacethe intersection of eventsjoint probabilitypopulation124. Which of the graph is used for a time series data:Select correct option:Frequency curveFrequency polygonHistorigramHistogram125. A histogram is consists of a set of adjacent rectangles whose bases are marked off by:Select correct option:Class boundariesClass limitsClass frequencyClass marks126. The value that has half of the observations above it and half the observations below it isknown as:Select correct option:MeanMedianModeStandard deviation127. The height of a student is 60 inches. This is an example of ...........?Select correct option:Continuous dataQualitative dataCategorical dataDiscrete data128. Range of the values -2,-3,-4,-3,-9,-2,-8,-1,0 isSelect correct option:0-9890-9=-9129. If the both tails of the distribution are equal, then distribution is called:Select correct option:J-shapedSymmetricalPositively SkewedNegatively Skewed130. Ranking scale also include the properties of which scale?

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Select correct option:Nominal scaleInterval scaleRatio scaleAll of these131. Range of the values -2.50,-3.70,-4.80,-3.10,-9.70,-2.20,-8.90,-1.60, 0.60 isSelect correct option:10.0310.309.109.000.60+9.70=10.30132. What is/are the mode for the following data: 1,m,d,n,,2,d,2,d,s,5,5,7Select correct option:2d52,d,5133. If the standard deviation of a population is 5.5, the population variance is:Select correct option:5.5312530.25134. What we commonly called a bell shaped distribution:Select correct option:symebi moderu shapskewed135. The beginnings of a cumulative frequency distribution are presented below. What is thenext number in the Cumulative Frequency column? Classes Frequency Cumulative Frequency6.1 to 8 1 1 8.1 to 10 2 10.1 to 12 3Select correct option:0123136. Range of the values -10,- 19, -9, -15, -28, -26, -25 is:Select correct option:+18-18-19+19137. Which one of the following is less than median for a symmetrical distribution:

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Select correct option:50percentile51 percentile2quartile4decile138. The value of the middle term in a ranked (ordered) data set is called theSelect correct option:modemeanmedianharmonic mean139. Sum of absolute deviations of the values is least when deviations are taken fromSelect correct option:meanmedianmodeg.m140. Statistic is a numerical quantity, which is calculated fromSelect correct option:dataobservationsamplepopulation141. The branch of Statistics that is concerned with the procedures and methodology forobtaining valid conclusions is called:Select correct option:descriptiveadvanceinfernetialsample142. How to find the class midpoint?Select correct option:Half the sum of upper class limit and lower class limitFind the difference between consecutive lower limitsCount the number of observations in the classDivide the class frequency by the number of observ143. For given data, discuss the shape of the distribution: X f 0.2 8 1.2 15 2.2 23 3.2 40Select correct option:Positively skewedNegatively skewedSymmetric curveU- Shaped curve144. Data classified by attributes are called:Select correct option:groupqulitative

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quantitivearrayif ‘2’ is a leading digit in 24335, than what are the trailing digits in the observation todisplay a ‘Stem-and –Leaf display’.Select correct option:4335433543145. A frequency polygon is obtained by plotting the class frequencies against what?Select correct option:classboundaycumulative frequencyrelative frequencymid point146. When more values are lying at the start of the distribution, it is:Select correct option:u shapepositivenegativesymmetrica147. The data for an ogive is found in which distribution:Select correct option:A cumulative frequency distributionA joint frequency distributionA frequency distributionA relative frequency distribution148. Which one of the following is greater than median for a symmetrical distribution:Select correct option:1st Decile7th Decile44th Percentile14th Percentile149. Statistics deals withSelect correct option:IndividualsIsolated itemsIsolated itemsAggregates of facts150. Data classified by attributes are called:Select correct option:Grouped dataQualitative dataQuantitative dataArrayed data

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151. As a general rule, statisticians tends to use which of the following number of classes whenarranging the dataSelect correct option:Fewer than 5Between 5 & 20Between 8 & 15More than 20152. The collection of all outcomes for an experiment is calledSelect correct option:a sample spacethe intersection of eventsjoint probabilitypopulation153. If P (E) is the probability that an event will occur, which of the following must be false:Select correct option:P(E)= - 1P(E)=1P(E)=1/2P(E)=1/3154. If we roll a die then probability of getting a ‘2’ will beSelect correct option:2/61/64/61155. In a multiplication theorem P (A n B) equals:Select correct option:P (A) P (B)P (A) + P (B)P (A) * P (B|A) pg 158P(B\A)*P(B)156. If Y=3X+5,then S.D of Y is equal toSelect correct option:9 s.d(x)3 s.d(x)s.d(x)+53s.d(x)+5157. In regression line Y=a+bX, X is called:Select correct option:Dependent variableIndependent variableExplained variableRegressand158. Symbolically, a marginal probability is:Select correct option:

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P(AB)P(AUB)P(A/B)P(A)159. Which formula represents the probability of the complement of event A:Select correct option:1 + P (A)1 - P (A)P (A)P (A) -1160. If A and B are independent events with P(A) = 0.05 and P(B) = 0.65, then P(A|B) = :Select correct option:0.650.050.030.07 not sure161. The probability of drawing a ‘white’ ball from a bag containing 4 red, 8 black and 3 whiteballs is:Select correct option:03/151/121/2Total ball= 4+8+3=15P=3/15162. An expected value of a random variable is equal to:Select correct option:VarianceMeanStandard deviationQuartile163. When we toss a fair coin 4 times, the sample space consists of….points.Select correct option:481216164. 5C5=Select correct option:511025165. In a probability distribution, the sum of the probabilities is equal to:Select correct option:

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00.10.51166. The simultaneous occurrence of two events is called:Select correct option:Joint probabilitySubjective probabilityPrior probabilityConditional probability167. Let E and F be events associated with the same experiment. Suppose the E and F areindependent and that P(E) = 1/4 and P(F) = 1/2 Then P(E U F) is:Select correct option:1/83/47/85/8¼+1/2=3/4




► Equally likely


► Exhaustive



►

377

►

►

►



► Rejected

► Accepted

► No conclusion

► Acknowledged



http://vustudents.ning.com

► Variances

► Means

► Proportions

► Groups


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► Helmert

► Pearson

► R.A Fisher

► Francis



► Z-test

► t-Test

► Both Z & T-test

► F test



► 0,1,2,3

► 1,3,3,1

► 1, 2, 3

► 3, 2

379


If X and Y are independent variables, then E (XY) is: http://vustudents.ning.com

► E(XX)

► E(X).E(Y)

► X.E(Y)

► Y.E(X)



► x & n

► x & p

► n & p

► x, n & p



► P(E)= - 1

► P(E)=1

► P(E)=1/2

► P(E)=1/3380


An estimator T is said to be unbiased estimator of if http://vustudents.ning.com

► E (T) =

► E (T) =T

► E (T) =0

► E (T) =1


The best unbiased estimator for population variance 2 is:

► Sample mean

► Sample median


► Sample variance

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The sample variance 2

2 ( )x xS

n

is:

► Unbiased estimator of 2



► None of these

Question No: 14 ( Marks: 1 ) http://vustudents.ning.com - Please choose one


1

0

c

-c

► 0

► 1

382

► c

► -c



( )g x is:

► ,f x y dx

► ,f x y dy

► ,f x y dx dy

► ,b d

a c

f x y dy dx


The analysis of variance technique is a method for : http://vustudents.ning.com


383












► Equal to 100


► Less than 100



384

The branch of Statistics that is concerned with the procedures and methodology for obtaining valid conclusions is called: http://vustudents.ning.com







► Classification

► Tabulation

► Bar chart




► 0.5

385

► 0.75

► 0.7979

► 0.6745


In normal distribution 2

► 1

► 2

► 3

► 0



► Ogive


► Frequency curve

► Historigram

Question No: 24 ( Marks: 1 ) http://vustudents.ning.com - Please choose one



386





When 1 32 4Q and Q ,what is the value of Median, if the distribution is

symmetrical:

► 1

► 2

► 3

► 4









► 5

387

► 8

► 9

► 10









► Type I error

► Type II error




388

How to find ( 1)P X Y ?

► f(0, 0) + f(0, 1) + f(1, 2)

► f(2, 0) + f(0, 1) + f(1, 0)

► f(0, 0) + f(1, 1) + f(1, 0)

► f(0, 0) + f(0, 1) + f(1, 0)



► Zero

► Less than 1

► Greater than 1

► Negative



►

►

►

389

►

www.vuzs.net

http://groups.google.com/group/vuzs



► 0 to 1

► 0 to -∞

► -∞ to +∞

► 0 to +∞


The total number of samples when sampling is done with replacement :

►

►

►

► 1


390


http://www.vuzs.net/


► Helmert

► Pearson

► R.A Fisher

► Francis


The test statistic used in analysis of variance procedure follow the ....... distribution.:

► χ2

► T

► Z

► F

www.vuzs.net




► Z-test

► t-Test

► Both Z & T-test

► F test

391





►

►

►

►


A die is rolled. What is the probability that the number rolled is greater than 2 and even:

► 1/2

► 1/3

► 2/3

► 5/6


The probability of drawing a king of spade from a pack of 52 cards is:

► 1/4

► 1/13

► 1/26

► 1/52

392

www.vuzs.net




► E (T) =

► E (T) =T

► E (T) =0

► E (T) =1


From point estimation, we always get:

► Single value

► Two values

► Range of values

► Zero393





► Sample mean

► Sample median


► Sample variance



1

0

c

-c

► 0

394

► 1

► c

► -c

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Var(4X + 5) =__________

► 16 Var (X)

► 16 Var (X) + 5

► 4 Var (X) + 5

► 12 Var (X)


When f(x) is continuous probability function, then P(X = 1) is:

► 1

395



►

►

► 0


The hyper geometric random variable is a(an):

► Continuous variable

► Discrete variable

► Undefined

► Independent variable


From a sample of 200 people were asked whether they like a particular product. Fifty said 'yes' and remain said 'no', assuming ‘yes’ means a success, which of the following is correct?

► Sample proportion p=0.33

► Sample proportion p=0.25

396

► Population proportion p= 0.33

► Population proportion p=0.25

www.vuzs.net



In any data set, what percent of values fall in the interval .Median Q D ?

► 50 per cent

► 68.5 per cent

► 95.4 per cent

► 99 per cent


If

► 0

► 20

► 5

► 25

397




The height of a student is 60 inches. This is an example of ...........?

► Continuous data

► Qualitative data

► Categorical data

► Discrete data


In Statistics, we have MSE which is abbreviation of……

► Mean square error

► Measured square error

► Medical screening exam

► Major sampling error


Which one is the formula of mid range:

►

398

►

►

►

www.vuzs.net



The deviation of a distribution from symmetry is called:

► Kurtosis

► Skewness

► Dispersion

► Flatness


If E is an impossible event, then P(E) is:

► 1

► 2

► 0

► 0.5

399




If a data set has the even number of observations, the median :

► Is the average value of the two middle items

► Can not be determined

► must be equal to the mean

► Is the average value of the two middle items when all items are arranged in ascending order


For the Poisson distribution

0.135 10.135( 1)

1!

eP X

the mean value is :

► 2

► 5

► 10

► 0.135



400





www.vuzs.net



Variance of the t-distribution is given by the formula:

►

►

►

►


If a continuous probability distribution has then what will be peakedness of

the distribution?

► Platykurtic

► Mesokurtic

► Leptokutic

► Moderately skewed401



Question # 1 of 10 ( Start time: 07:10:27 PM ) Total Marks: 1 When two dice are rolled the number of possible sample points is : Select correct option: 6 12 24 36

Question # 2 of 10 ( Start time: 07:11:18 PM ) Total Marks: 1 A fair coin is tossed three times, the probability that at least one head appear is: Select correct option: 1/8 7/8 3/8 5/8 Question # 3 of 10 ( Start time: 07:12:14 PM ) Total Marks: 1 In scatter diagram, the variable plotted along Y-axis is: Select correct option: Independent variable Dependent variable Continuous variable Discrete variable of the following is not a measure of central tendency? Select correct option: Percentile Quartile Standard deviation Mode Which of the following is NOT a possible probability? Select correct option:

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25/100 1.25 0 1

Question # 6 of 10 ( Start time: 07:16:06 PM ) Total Marks: 1 Evaluate (10-4)! Select correct option: 1000 720 480 32

Question # 7 of 10 ( Start time: 07:17:34 PM ) Total Marks: 1 When E is an impossible event, then P(E) is: Select correct option: 0 1 2 0.5

Question # 8 of 10 ( Start time: 07:19:00 PM ) Total Marks: 1 The probability of drawing a ‘white’ ball from a bag containing 4 red, 8 black and 3 white balls is: Select correct option: 0 3/15 1/12 1/2

standard deck of 52 cards is shuffled. What is the probability of choosing the 5 of diamonds: Select correct option: 1/5 1/13 5/52

403

1/52

If we roll three fair dices then the total number of outcomes is: Select correct option: 6 36 216 1296

Question No: 1 ( Marks: 1 ) - Please choose oneMean deviation is always:

► Less than S.D► Greater than S.D► Greater or equal to S.D► Less or equal to S.D

Question No: 2 ( Marks: 1 ) - Please choose oneThe value of χ2can never be :

► Zero► Less than 1► Greater than 1► Negative

Question No: 3 ( Marks: 1 ) - Please choose oneThe mean of the F-distribution is:

► ► ► ►

Question No: 4 ( Marks: 1 ) - Please choose oneIf X and Y are random variables, then is equal to:

► ► ► ►

404

Question No: 5 ( Marks: 1 ) - Please choose oneEvaluate: (9-4)!► 362880► 120► 24► 6

Question No: 6 ( Marks: 1 ) - Please choose oneWhich formula represents the probability of the complement of event A:► 1 + P (A)► 1 - P (A)► P (A)► P (A) -1

Question No: 7 ( Marks: 1 ) - Please choose oneIdeally the width of confidence interval should be:

► 0► 1► 99► 100

Question No: 8 ( Marks: 1 ) - Please choose oneIf the sampling distribution of is normal, the interval includes:


► 99.73% of the sample means



Question No: 9 ( Marks: 1 ) - Please choose oneThe probability distribution of a statistic is called the:

► Population distribution

► Frequency distribution ► Sampling distribution

► Sample distribution


405


► E (T) =

► E (T) =T

► E (T) =0

► E (T) =1

Question No: 11 ( Marks: 1 ) - Please choose oneIf the following is a probability distribution, then what is the value of 'a':

X 1 2 3

P(X) 0.1 a 0.1

► 0.6► 0.8► 0.2► 0.4

Question No: 12 ( Marks: 1 ) - Please choose oneA discrete probability function f(x) is always:

► Non-negative► Negative► One► Zero

Question No: 13 ( Marks: 1 ) - Please choose oneAn expected value of a random variable is equal to:

► Variance► Mean

406

► Standard deviation► Covariance

Question No: 14 ( Marks: 1 ) - Please choose oneThe __________:

► ► ► ►

Question No: 15 ( Marks: 1 ) - Please choose oneThe area under a normal curve between 0 and -1.75 is

► .0401

► .5500

► .4599► .9599

Question No: 16 ( Marks: 1 ) - Please choose oneThe continuity correction factor is used when:

► The sample size is at least 5► Both nP and n (1-P) are at least 30► A continuous distribution is used to approximate a discrete distribution► The standard normal distribution is applied

Question No: 17 ( Marks: 1 ) - Please choose oneWhich of the following is impossible in sampling:

► Destructive tests► Heterogeneous► To make voters list► None of these

Question No: 18 ( Marks: 1 ) - Please choose oneWhich of the following is a systematic arrangement of data into rows and columns?► Classification► Tabulation► Bar chart► Component bar chart

407

Question No: 19 ( Marks: 1 ) - Please choose oneWhich one of the following statements is true regarding a sample?► It is a part of population► It must contain at least five observations► It refers to descriptive statistics► It produces True value

Question No: 20 ( Marks: 1 ) - Please choose oneThe data for an ogive is found in which distribution?► A relative frequency distribution► A frequency distribution► A joint frequency distribution► A cumulative frequency distribution

Question No: 1 ( Marks: 1 ) - Please choose oneWhen each outcome of a sample space has equal chance to occur as any other, the outcomes are called:► Mutually exclusive► Equally likely► Not mutually exclusive► Exhaustive

Question No: 2 ( Marks: 1 ) - Please choose oneThe mean of the F-distribution is:

► ► ► ►

Question No: 3 ( Marks: 1 ) - Please choose oneThe LSD test is applied only if the null hypothesis is:

► Rejected► Accepted► No conclusion► Acknowledged

Question No: 4 ( Marks: 1 ) - Please choose oneAnalysis of variance is a procedure that enables us to test the equality of several:

► Variances► Means► Proportions► Groups

408

Question No: 5 ( Marks: 1 ) - Please choose oneANOVA was introduced by :

► Helmert► Pearson► R.A Fisher► Francis

Question No: 6 ( Marks: 1 ) - Please choose oneFor testing of hypothesis about population proportion , we use:

► Z-test► t-Test► Both Z & T-test► F test

Question No: 7 ( Marks: 1 ) - Please choose oneIf a random variable X denotes the number of heads when three distinct coins are tossed, the X assumed the values:

► 0,1,2,3► 1,3,3,1► 1, 2, 3► 3, 2

Question No: 8 ( Marks: 1 ) - Please choose oneIf X and Y are independent variables, then E (XY) is:

► E(XX) ► E(X).E(Y)► X.E(Y)► Y.E(X)

Question No: 9 ( Marks: 1 ) - Please choose oneThe parameters of the binomial distribution b(x; n, p) are:

► x & n► x & p► n & p► x, n & p

Question No: 10 ( Marks: 1 ) - Please choose oneIf P (E) is the probability that an event will occur, which of the following must be false:► P(E)= - 1

409

► P(E)=1► P(E)=1/2► P(E)=1/3

Question No: 11 ( Marks: 1 ) - Please choose oneAn estimator T is said to be unbiased estimator of if

► E (T) =

► E (T) =T

► E (T) =0

► E (T) =1

Question No: 12 ( Marks: 1 ) - Please choose oneThe best unbiased estimator for population variance is:

► Sample mean

► Sample median


► Sample variance

Question No: 13 ( Marks: 1 ) - Please choose oneThe sample variance is:




► None of these

Question No: 14 ( Marks: 1 ) - Please choose oneWhen c is a constant, then E(c) is:

10c-c

410

► 0► 1► c► -c

Question No: 15 ( Marks: 1 ) - Please choose oneIf f (x, y) is bivariate probability density function of continuous r.v.'s X and Y thenis:

► ► ► ►

Question No: 16 ( Marks: 1 ) - Please choose oneThe analysis of variance technique is a method for :

► Comparing F distributions ► Comparing three or more means ► Measuring sampling error ► Comparing variances

Question No: 17 ( Marks: 1 ) - Please choose oneThe continuity correction factor is used when:

► The sample size is at least 5► Both nP and n (1-P) are at least 30► A continuous distribution is used to approximate a discrete distribution► The standard normal distribution is applied

Question No: 18 ( Marks: 1 ) - Please choose oneStem and leaf is more informative when data is :► Equal to 100


► Less than 100


Question No: 19 ( Marks: 1 ) - Please choose oneThe branch of Statistics that is concerned with the procedures and methodology for obtaining valid conclusions is called:

411

► Descriptive Statistics► Advance Statistics► Inferential Statistics


Question No: 20 ( Marks: 1 ) - Please choose oneWhich of the following is a systematic arrangement of data into rows and columns?► Classification► Tabulation► Bar chart► Component bar chart

Question No: 21 ( Marks: 1 ) - Please choose oneIn normal distribution Q.D =

► ► ► ►

Question No: 22 ( Marks: 1 ) - Please choose oneIn normal distribution

► 1► 2► 3► 0

Question No: 23 ( Marks: 1 ) - Please choose oneIf you connect the mid-points of rectangles in a histogram by a series of lines that also touches the x-axis from both ends, what will you get?

► Ogive► Frequency polygon► Frequency curve► Historigram

Question No: 24 ( Marks: 1 ) - Please choose oneWhich one of the following statements is true regarding a population?► It must be a large number of values► It must refer to people► It is a collection of individuals, objects, or measurements

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Question No: 25 ( Marks: 1 ) - Please choose oneWhen ,what is the value of Median, if the distribution is symmetrical:

► 1► 2► 3► 4

Question No: 26 ( Marks: 1 ) - Please choose oneIn a simple linear regression model, if it is assumed that the intercept parameter is equal to zero, then:► The regression line will pass through the origin► The regression line will pass through the point (0,10).► The regression line will pass through the point (0,-10).► The slope of the line will also be equal to 0.

Question No: 27 ( Marks: 1 ) - Please choose oneThe degrees of freedom for a t-test with sample size 10 is:

► 5► 8► 9► 10

Question No: 28 ( Marks: 1 ) - Please choose oneIn testing of hypothesis, we always begin it with assuming that:

► Null hypothesis is true► Alternative hypothesis is true► Sample size is large► Population is normal

Question No: 29 ( Marks: 1 ) - Please choose oneA failing student is passed by an examiner is an example of:

► Type I error

► Type II error



Question No: 30 ( Marks: 1 ) - Please choose oneHow to find ?

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► f(0, 0) + f(0, 1) + f(1, 2)► f(2, 0) + f(0, 1) + f(1, 0)► f(0, 0) + f(1, 1) + f(1, 0)► f(0, 0) + f(0, 1) + f(1, 0)


10! =………….

► 362880 ► 3628800 ► 362280 ► 362800 Question No: 2 ( Marks: 1 ) - Please choose one

When E is an impossible event, then P(E) is:

► 2 ► 0 ► 0.5 ► 1



► Zero ► Less than 1 ► Greater than 1 ► Negative


The curve of the F- distribution depends upon:

► Degrees of freedom ► Sample size ► Mean ► Variance Question No: 5 ( Marks: 1 ) - Please choose one


414

►

►

►

► Question No: 6 ( Marks: 1 ) - Please choose one

In testing hypothesis, we always begin it with assuming that:

► Null hypothesis is true ► Alternative hypothesis is true ► Sample size is large ► Population is normal Question No: 7 ( Marks: 1 ) - Please choose one

For the Poisson distribution P(x) = the mean value

is : ► 2 ► 5

► 10 ► 0.135


When two coins are tossed simultaneously, P (one head) is:

►

1

4

►

1

2

►

3

4

► 1 Question No: 9 ( Marks: 1 ) - Please choose one

From point estimation, we always get:

► Single value

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► Two values

► Range of values

► Zero






► None of these


Var(4X + 5) =__________

► 16 Var (X) ► 16 Var (X) + 5 ► 4 Var (X) + 5 ► 12 Var (X) Question No: 12 ( Marks: 1 ) - Please choose one

When f (x, y) is bivariate probability density function of continuous r.v.'s X and Y, then

is equal to:

► 1 ► 0 ► -1 ► Question No: 13 ( Marks: 1 ) - Please choose one


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► .0401

► .5500


When a fair die is rolled, the sample space consists of:

► 2 outcomes ► 6 outcomes ► 36 outcomes

► 16 outcomes Question No: 15 ( Marks: 1 ) - Please choose one

When testing for independence in a contingency table with 3 rows and 4 columns, there are ________ degrees of freedom. ► 5 ► 6 ► 7 ► 12 Question No: 16 ( Marks: 1 ) - Please choose one

The F- test statistic in one-way ANOVA is: ► SSW / SSE ► MSW / MSE ► SSE / SSW ► MSE / MSW Question No: 17 ( Marks: 1 ) - Please choose one







A uniform distribution is defined by:

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► Its largest and smallest value

► Smallest value

► Largest value

► Mid value


Which graph is made by plotting the mid point and frequencies?


► Ogive

► Histogram

► Frequency curve


In a set of 20 values all the values are 10, what is the value of median?

► 2 ► 5 ► 10 ► 20

STA301 Online 5 Quizzes from Lectures 1-27 Shared by Shazia , sent by Waqas


If Y=bX, then variance of Y isSelect correct option: b*2 var(x) var(x) b var(x)

b square root var(x)

2. Question # 2 of 10 ( Start time: 08:24:38 PM ) Total Marks: 1If f(x) is a continuous probability function, then P(X = 2) is:

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Select correct option: 1 0 1/2 2



If A and B are mutually exclusive events with P (A) =0.25 and P (B) = 0.50, Then P (A or B) =………Select correct option: 0.25 0.75 0.50 1



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8. Question # 8 of 10 ( Start time: 08:31:42 PM ) Total Marks: 1If Y=3X+5,then S.D of Y is equal toSelect correct option: 9 s.d(x) 3 s.d(x) s.d(x)+5 3s.d(x)+5

Question # 9 of 10 ( Start time: 08:33:16 PM ) Total Marks: 1

The probability of drawing a red queen card from well-shuffled pack of 52 playing cards isSelect correct option: 4/52 2/52 13/52 26/52

10. Question # 10 of 10 ( Start time: 08:34:40 PM ) Total Marks: 1If P (B|A) = 0.25 and P (A and B) =0.20, then P (A) isSelect correct option: 0.05 0.80 0.95 0.75

11. Question # 1 of 10 ( Start time: 08:57:45 PM ) Total Marks: 1When a coin is tossed 3 times, the probability of getting 3 tails isSelect correct option: 1/8 3/8 3/6 2/8

12. Question # 2 of 10 ( Start time: 08:59:14 PM ) Total Marks: 1In how many ways can a team of 11 players be chosen from a total of 16 players?

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Select correct option: 4368(not confirmed) 2426 5400 2680


The standard deviation of c (constant) isSelect correct option: c c square 0 does not exist

14. Question # 4 of 10 ( Start time: 09:01:46 PM ) Total Marks: 1If P (E) is the probability that an event will occur, which of the following must be false:Select correct option: P(E)= - 1 P(E)=1 P(E)=1/2 P(E)=1/3


Let E and F be events associated with the same experiment. Suppose the E and F are independent and that P(E) = 1/4 and P(F) = 1/2 Then P(E U F) is:Select correct option: 1/8 3/4 7/8 5/8

16. Question # 6 of 10 ( Start time: 09:04:09 PM ) Total Marks: 1A student solved 25 questions from first 50 questions of a book to be solved. The probability that he will solve the remaining all questions is:Select correct option: 0.25 0.5 1 0

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18. Question # 9 of 10 ( Start time: 09:07:48 PM ) Total Marks: 1The classical definition of probability assumes:Select correct option: Exhaustive events Mutually exclusive events Equally likely evens Independent evens

19. Question # 10 of 10 ( Start time: 09:08:50 PM ) Total Marks: 1In scatter diagram, the variable plotted along Y-axis is:Select correct option: Independent variable Dependent variable Continuous variable Discrete variable

20. Which of the following measures of dispersion are based on deviations from the mean? Select correct option:


All of the these

21. What does it mean when a data set has a standard deviation equal to zero?


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23. Which of the following can never be probability of an event? Select correct option:

0 1 0.5 -0.5

24. The standard deviation of -1, -1, -1, -1 will be Select correct option:


25. Which formula represents the probability of the complement of event A: Select correct option:

1 + P (A) 1 - P (A) P (A) P (A) -1

26. The Special Rule of Addition is used to combine: Select correct option:

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28. E(4X + 5) =________ Select correct option:

12 E (X) 4 E (X) + 5 16 E (X) + 5 16 E (X)

29. When two dice are rolled the number of possible sample points is : Select correct option:

6 12 24 36

30. Question # 1 of 10 ( Start time: 09:43:04 PM ) Total Marks: 1 If two events A and B are not mutually exclusive then Select correct option:


P (A or B) = P (A) + P (B)

P (A or B) = P (A) x P (B)

P (A or B) = P (A) + P (B)

31.

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Question # 2 of 10 ( Start time: 09:43:59 PM ) Total Marks: 1 Evaluate (10-4)! Select correct option:

1000 720 480 32

32. Question # 3 of 10 ( Start time: 09:45:01 PM ) Total Marks: 1 When E is an impossible event, then P(E) is: Select correct option:

0 1 2 0.5

33. Question # 4 of 10 ( Start time: 09:46:20 PM ) Total Marks: 1 When we toss a coin , we get only: Select correct option:


34.

Question # 5 of 10 ( Start time: 09:47:15 PM ) Total Marks: 1 For exhaustive events, the P(AUBUC) is equal to: Select correct option:

P(A) P(S) P(A) * P(B)* P(C) P(B)

35. Question # 6 of 10 ( Start time: 09:48:21 PM ) Total Marks: 1 A student solved 25 questions from first 50 questions of a book to be solved. The probability that he will solve the remaining all questions is: Select correct option:

0.25 425

0.5 1 0



37.

Question # 9 of 10 ( Start time: 09:50:35 PM ) Total Marks: 1 If we roll a die then probability of getting a ‘6’ will be Select correct option:

2/6

1/6

4/6

1

38. Question # 10 of 10 ( Start time: 09:51:36 PM ) Total Marks: 1 If P(A) = 0.45, P(B) = 0.35, and P(A and B) = 0.25, then P(A | B) is: Select correct option:

1.4 1.8 0.714 0.556

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39. Question # 8 of 10 ( Start time: 09:49:53 PM ) Total Marks: 1 Which of the following is not a measure of central tendency? Select correct option:

Percentile

Quartile

Standard deviation

Mode

40. Question # 1 of 10 ( Start time: 09:56:49 PM ) Total Marks: 1 Random experiment can be repeated any no. of times under the……… conditions. Select correct option:

Different Similar

42. Question # 3 of 10 ( Start time: 09:58:41 PM ) Total Marks: 1 The simultaneous occurrence of two events is called: Select correct option:


43. Question # 4 of 10 ( Start time: 09:59:47 PM ) Total Marks: 1 In regression analysis, the variable that is being predicted is the Select correct option:

Dependent variable



None of these

427

a)

Solution:

An array is a systematic arrangement of objects, usually in rows and columns.

(b)

Make discrete frequency distribution from the given data,

1,2,3,2,1,2,1,3, 4,5,1,2,3,1,4,2, 2,3,2,1,4,4,4,2,1,

Also find;

Cumulative frequencies

Relative frequencies

Solution:

CLASS NO. Frequencies Cumulative frequency

Relative frequency

1 7 7 0.28

2 8 7+8 = 15 0.32

3 4 15+4 =19 0.16

4 5 19+5 = 24 0.2

5 1 24+1 = 25 0.04

Total 25 ----

Question no.02

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(a) Find Geometric mean from the following data.

1, 2, 3,2,4,5,4,3,4,-1,4, 3,0,1,-3, 2,4

Solution:

Geometric mean can not b calculated as there are some negative values and zero values present in the data.

(b) The weight of the 40 male students at a university is given in the following frequency table:

Calculate median and mode from the above data.

Weight Class Boundary frequency CF

118-126 117.5 – 126.5 3 3

127-135 126.5 – 135.5 5 3+5 = 8

136-144 135.5 – 144.5 9 8+9 = 17

145-153 144.5 – 153.5 12 17+12 = 29

154-162 153.5 – 162.5 5 29+5 = 34

163-171 162.5 – 171.5 4 34+4 = 38

172-180 171.5 – 180.5 238+2 =40

(equal to the sum of total frequency.. !

Solution:

429

MODE:

Where l=144.5 , h =9 , fm= 12 , f1 = 9 , f 2 = 5

MEDIAN:

Where l=144.5, h=9, f=12, n/2=20 and c = 17

Put these values in formal and then calculate…

Question no.03

(b) For given data calculate range and coefficient of range,

430

0.035, 0.045, 0.031, 0.044, 0.032

Solution:

Xm=0.045

X0=0.031

Range: =

Coefficient of range: =

Put the values in the formula then calculate

(c) Calculate an appropriate measure of dispersion for the following data.

Farm Size (acre)

No. of Farms

Bellow 40 394

41-80 461

81-120 391

121-160 334

161-200 169

201-240 113

241 and above

148

Solution:

431

Question solve with quartile deviation;;;

Quartile deviation = Q3 - Q1 / 2

My Dear friend in blue line are correct if u have any problem in these Questions that call me at my number 0312 4070263

a) Area Table

For if we have two tail tests. Just see this value

in the cumulative table that is 2.33.

b) BASIC Derivative Formulas/Rules:

Derivatives are solved according to some specific rules/formulas. You need to remember them. Three very BASIC rules are.

1) Derivative of a constant is always ZERO.

2) Derivative of a variable x with respect to x, is always x.

3) And derivative of a exponential is given by following rule.

432

For some more basic formulas, you can click here

c) Binomial distribution:

Many times we deal with situation where a g group can be categorized into two mutually exclusive subgroups, e.g. sick and not sick, male and female, success and failure. Distribution of such data will be called binomial distribution.

Binomial population:

A population which can be divided into a binomial distribution.

Confidence interval for binomial distribution:

We may use the confidence interval method to estimate the value of parameter of binomial distribution. For example, Population proportion can be found out with by this formula.

d) combinationHere in the example we will use the combination rule to find the number of outcomes

The sample space S contains

sample points

433

http://www.sosmath.com/tables/derivative/derivative.html

ways of selecting four items out of twelve

The box contains 3 faulty and 9 good items. The box is accepted if there is (i) no faulty items, or (ii) one faulty item in the sample of 4 items selected.

As a hint, remember when the word “or” is used between two events then we add their probabilities.

Let A denote the event the number of faulty items chosen is 0 or 1.

Then

e) Explanation of Double Integral (Example in Lesson # 26)

The double integral is

Putting the value of f(x,y) [given]

For a moment consider x and dx as constant factor and ONLY integrate it w.r.t dy

434

Now integrate this w.r.t dx

[Note: w.r.t is abbreviation of with respect to]

f) Takin power

In the above picture the buttons in the circle can be used to take power, base and the both at a time as well, specially the button with arrow sign can be used to take the power, press this button and type the digit which you want to take as power.

Hope you get the idea and now would be able to use it.

g) Finding the critical value using the table of standard normal distribution

435

Finding the critical value using the table of standard normal distribution (Z table)

1) If critical value or 0.05 then this imply that confidence level is 95% or 0.95

2) If we have TWO tail tests, this mean half of 0.95 will lie on each side normal distribution. The half of is 0.95/2= 0.4750. Now we need to find that value of Z under which this area value of 0.4750 lies.

3) In the area table of normal distribution (available below), inside the rows and columns, locate the value of 0.4750

4) Note down which row and column are crossing this value? You will see the row “1.9” and column “0.06” are crossing this value. {This is called the inverse use of area table}

5) Now combined these two values, you will get 1.96.

6) So this mean that the table value of Z that contain .4750 area is Z=1.96.

7) Since we have TWO tail test and normal distribution is symmetric so we will say on the left side of curve this value will be -1.96 and on the right side of the curve the value will be +1.96.

DO YOURSELF:

Try to find value of for TWO tail test, by adopting this process from step 1 through 7

436

For single sided test (one tail test), do the same procedure BUT omit the step 2 and 7

You can also find this table at http://business.statistics.sweb.cz/normal.jpg

INTEGRATION FORMULAS

This page contains a list of very commonly used integration formulas.

437

http://business.statistics.sweb.cz/normal.jpg

b) Area Table

For if we have two tail tests. Just see this value

in the cumulative table that is 2.33.

b) BASIC Derivative Formulas/Rules:

Derivatives are solved according to some specific rules/formulas. You need to remember them. Three very BASIC rules are.

1) Derivative of a constant is always ZERO.

2) Derivative of a variable x with respect to x, is always x.

438

1.

2.

(where is a constant)

3.

4. Integration by Substitution

where and

Also written as:

5.

6.

7.

3) And derivative of a exponential is given by following rule.

For some more basic formulas, you can click here

h) Binomial distribution:

Many times we deal with situation where a g group can be categorized into two mutually exclusive subgroups, e.g. sick and not sick, male and female, success and failure. Distribution of such data will be called binomial distribution.

Binomial population:

A population which can be divided into a binomial distribution.

Confidence interval for binomial distribution:

We may use the confidence interval method to estimate the value of parameter of binomial distribution. For example, Population proportion can be found out with by this formula.

i) combinationHere in the example we will use the combination rule to find the number of outcomes

The sample space S contains

439

http://www.sosmath.com/tables/derivative/derivative.html

sample points

ways of selecting four items out of twelve

The box contains 3 faulty and 9 good items. The box is accepted if there is (i) no faulty items, or (ii) one faulty item in the sample of 4 items selected.

As a hint, remember when the word “or” is used between two events then we add their probabilities.

Let A denote the event the number of faulty items chosen is 0 or 1.

Then

j) Explanation of Double Integral (Example in Lesson # 26)

440

The double integral is

Putting the value of f(x,y) [given]

For a moment consider x and dx as constant factor and ONLY integrate it w.r.t dy

Now integrate this w.r.t dx

[Note: w.r.t is abbreviation of with respect to]

k) Takin power

441

In the above picture the buttons in the circle can be used to take power, base and the both at a time as well, specially the button with arrow sign can be used to take the power, press this button and type the digit which you want to take as power.

Hope you get the idea and now would be able to use it.

l) Finding the critical value using the table of standard normal distribution

Finding the critical value using the table of standard normal distribution (Z table)

1) If critical value or 0.05 then this imply that confidence level is 95% or 0.95

2) If we have TWO tail tests, this mean half of 0.95 will lie on each side normal distribution. The half of is 0.95/2= 0.4750. Now we need to find that value of Z under which this area value of 0.4750 lies.

3) In the area table of normal distribution (available below), inside the rows and columns, locate the value of 0.4750

442

4) Note down which row and column are crossing this value? You will see the row “1.9” and column “0.06” are crossing this value. {This is called the inverse use of area table}

5) Now combined these two values, you will get 1.96.

6) So this mean that the table value of Z that contain .4750 area is Z=1.96.

7) Since we have TWO tail test and normal distribution is symmetric so we will say on the left side of curve this value will be -1.96 and on the right side of the curve the value will be +1.96.

DO YOURSELF:

Try to find value of for TWO tail test, by adopting this process from step 1 through 7

For single sided test (one tail test), do the same procedure BUT omit the step 2 and 7

You can also find this table at http://business.statistics.sweb.cz/normal.jpg

443

http://business.statistics.sweb.cz/normal.jpg

INTEGRATION FORMULAS

This page contains a list of very commonly used integration formulas.

444

1.

2.

(where is a constant)

3.

4. Integration by Substitution

where and

Also written as:

5.

6.

7.

STA301 Qezz no 1

Quiz Start Time: 05:01 PM

Time Left 81

sec(s)


What type of data is collected in population census?


Two Types

Quiz Start Time: 05:01 PM Time Left 77

sec(s)


The collection of all outcomes for an experiment is called


a sample space

the intersection of events

joint probability

population


sec(s)


445

Which of the graph is used for a time series data:


Frequency curve

Frequency polygon

Historigram

Histogram ( not sure)


sec(s)


A histogram is consists of a set of adjacent rectangles whose bases are marked off by:


Class boundaries

Class limits

Class frequency

Class marks


sec(s)


446

The value that has half of the observations above it and half the observations below it is known as:


Mean

Median

Mode

Standard deviation


sec(s)


The height of a student is 60 inches. This is an example of ...........?


Continuous data

Qualitative data

Categorical data

Discrete data


sec(s)

447


Range of the values -2,-3,-4,-3,-9,-2,-8,-1,0 is


0

-9

8

9


sec(s)


If the both tails of the distribution are equal, then distribution is called:


J-shaped

Symmetrical

Positively Skewed

Negatively Skewed


sec(s)

448


Ranking scale also include the properties of which scale?


Nominal scale

Interval scale

Ratio scale

All of these


sec(s)


Range of the values -2.50,-3.70,-4.80,-3.10,-9.70,-2.20,-8.90,-1.60, 0.60 is


10.03

10.30

9.10

9.00

STA 301 All Definitions

449

(Muhammad Rashid Chishti)

Statistics - a set of concepts, rules, and procedures that help us to: o organize numerical information in the form of tables, graphs, and

charts; ounderstand statistical techniques underlying decisions that affect our

lives and well-being; and omake informed decisions.

Data - facts, observations, and information that come from investigations. oMeasurement data sometimes called quantitative data -- the result of

using some instrument to measure something (e.g., test score, weight); oCategorical data also referred to as frequency or qualitative data.

Things are grouped according to some common property(ies) and the number of members of the group are recorded (e.g., males/females, vehicle type).

Variable - property of an object or event that can take on different values. For example, college major is a variable that takes on values like mathematics, computer science, English, psychology, etc.

oDiscrete Variable - a variable with a limited number of values (e.g., gender (male/female), college class (freshman/sophomore/junior/senior).

oContinuous Variable - a variable that can take on many different values, in theory, any value between the lowest and highest points on the measurement scale.

o Independent Variable - a variable that is manipulated, measured, or selected by the researcher as an antecedent condition to an observed behavior. In a hypothesized cause-and-effect relationship, the independent variable is the cause and the dependent variable is the outcome or effect.

oDependent Variable - a variable that is not under the experimenter's control -- the data. It is the variable that is observed and measured in response to the independent variable.

oQualitative Variable - a variable based on categorical data. oQuantitative Variable - a variable based on quantitative data.

Graphs - visual display of data used to present frequency distributions so that the shape of the distribution can easily be seen.

oBar graph - a form of graph that uses bars separated by an arbitrary amount of space to represent how often elements within a category occur. The higher the bar, the higher the frequency of occurrence. The underlying measurement scale is discrete (nominal or ordinal-scale data), not continuous.

oHistogram - a form of a bar graph used with interval or ratio-scaled data. Unlike the bar graph, bars in a histogram touch with the width of the bars defined by the upper and lower limits of the interval. The

450

measurement scale is continuous, so the lower limit of any one interval is also the upper limit of the previous interval.

oBoxplot - a graphical representation of dispersions and extreme scores. Represented in this graphic are minimum, maximum, and quartile scores in the form of a box with "whiskers." The box includes the range of scores falling into the middle 50% of the distribution (Inter Quartile Range = 75th percentile - 25th percentile)and the whiskers are lines extended to the minimum and maximum scores in the distribution or to mathematically defined (+/-1.5*IQR) upper and lower fences.

oScatterplot - a form of graph that presents information from a bivariate distribution. In a scatterplot, each subject in an experimental study is represented by a single point in two-dimensional space. The underlying scale of measurement for both variables is continuous (measurement data). This is one of the most useful techniques for gaining insight into the relationship between tw variables.

Measures of Center - Plotting data in a frequency distribution shows the general shape of the distribution and gives a general sense of how the numbers are bunched. Several statistics can be used to represent the "center" of the distribution. These statistics are commonly referred to as measures of central tendency.

oMode - The mode of a distribution is simply defined as the most frequent or common score in the distribution. The mode is the point or value of X that corresponds to the highest point on the distribution. If the highest frequency is shared by more than one value, the distribution is said to be multimodal. It is not uncommon to see distributions that are bimodal reflecting peaks in scoring at two different points in the distribution.

oMedian - The median is the score that divides the distribution into halves; half of the scores are above the median and half are below it when the data are arranged in numerical order. The median is also referred to as the score at the 50th percentile in the distribution. The median location of N numbers can be found by the formula (N + 1) / 2. When N is an odd number, the formula yields a integer that represents the value in a numerically ordered distribution corresponding to the median location. (For example, in the distribution of numbers (3 1 5 4 9 9 8) the median location is (7 + 1) / 2 = 4. When applied to the ordered distribution (1 3 4 5 8 9 9), the value 5 is the median, three scores are above 5 and three are below 5. If there were only 6 values (1 3 4 5 8 9), the median location is (6 + 1) / 2 = 3.5. In this case the median is half-way between the 3rd and 4th scores (4 and 5) or 4.5.

oMean - The mean is the most common measure of central tendency and the one that can be mathematically manipulated. It is defined as the average of a distribution is equal to the X / N. Simply, the mean is computed by summing all the scores in the distribution (X) and dividing that sum by the total number of scores (N). The mean is the

451

balance point in a distribution such that if you subtract each value in the distribution from the mean and sum all of these deviation scores, the result will be zero.

Measures of Spread - Although the average value in a distribution is informative about how scores are centered in the distribution, the mean, median, and mode lack context for interpreting those statistics. Measures of variability provide information about the degree to which individual scores are clustered about or deviate from the average value in a distribution.

oRange - The simplest measure of variability to compute and understand is the range. The range is the difference between the highest and lowest score in a distribution. Although it is easy to compute, it is not often used as the sole measure of variability due to its instability. Because it is based solely on the most extreme scores in the distribution and does not fully reflect the pattern of variation within a distribution, the range is a very limited measure of variability.

o Interquartile Range (IQR) - Provides a measure of the spread of the middle 50% of the scores. The IQR is defined as the 75th percentile - the 25th percentile. The interquartile range plays an important role in the graphical method known as the boxplot. The advantage of using the IQR is that it is easy to compute and extreme scores in the distribution have much less impact but its strength is also a weakness in that it suffers as a measure of variability because it discards too much data. Researchers want to study variability while eliminating scores that are likely to be accidents. The boxplot allows for this for this distinction and is an important tool for exploring data.

oVariance - The variance is a measure based on the deviations of individual scores from the mean. As noted in the definition of the mean, however, simply summing the deviations will result in a value of 0. To get around this problem the variance is based on squared deviations of scores about the mean. When the deviations are squared, the rank order and relative distance of scores in the distribution is preserved while negative values are eliminated. Then to control for the number of subjects in the distribution, the sum of the squared deviations, (X - X), is divided by N (population) or by N - 1 (sample). The result is the average of the sum of the squared deviations and it is called the variance.

oStandard deviation - The standard deviation (s or ) is defined as the positive square root of the variance. The variance is a measure in squared units and has little meaning with respect to the data. Thus, the standard deviation is a measure of variability expressed in the same units as the data. The standard deviation is very much like a mean or an "average" of these deviations. In a normal (symmetric and mound-shaped) distribution, about two-thirds of the scores fall between +1 and -1 standard deviations from the mean and the standard deviation is approximately 1/4 of the range in small samples (N < 30) and 1/5 to 1/6 of the range in large samples (N > 100).

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Measures of Shape - For distributions summarizing data from continuous measurement scales, statistics can be used to describe how the distribution rises and drops.

oSymmetric - Distributions that have the same shape on both sides of the center are called symmetric. A symmetric distribution with only one peak is referred to as a normal distribution.

oSkewness - Refers to the degree of asymmetry in a distribution. Asymmetry often reflects extreme scores in a distribution.

Positively skewed - A distribution is positively skewed when is has a tail extending out to the right (larger numbers) When a distribution is positively skewed, the mean is greater than the median reflecting the fact that the mean is sensitive to each score in the distribution and is subject to large shifts when the sample is small and contains extreme scores.

Negatively skewed - A negatively skewed distribution has an extended tail pointing to the left (smaller numbers) and reflects bunching of numbers in the upper part of the distribution with fewer scores at the lower end of the measurement scale.

oKurtosis - Like skewness, kurtosis has a specific mathematical definition, but generally it refers to how scores are concentrated in the center of the distribution, the upper and lower tails (ends), and the shoulders (between the center and tails) of a distribution.

Mesokurtic - A normal distribution is called mesokurtic. The tails of a mesokurtic distribution are neither too thin or too thick, and there are neither too many or too few scores in the center of the distribution.

Platykurtic - Starting with a mesokurtic distribution and moving scores from both the center and tails into the shoulders, the distribution flattens out and is referred to as platykurtic.

Leptokurtic - If you move scores from shoulders of a mesokurtic distribution into the center and tails of a distribution, the result is a peaked distribution with thick tails. This shape is referred to as leptokurtic.

Discrete Data

A set of data is said to be discrete if the values / observations belonging to it are distinct and separate, i.e. they can be counted (1,2,3,....). Examples might include the number of kittens in a litter; the number of patients in a doctors surgery; the number of flaws in one metre of cloth; gender (male, female); blood group (O, A, B, AB).

Compare continuous data.

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Categorical Data

A set of data is said to be categorical if the values or observations belonging to it can be sorted according to category. Each value is chosen from a set of non-overlapping categories. For example, shoes in a cupboard can be sorted according to colour: the characteristic 'colour' can have non-overlapping categories 'black', 'brown', 'red' and 'other'. People have the characteristic of 'gender' with categories 'male' and 'female'.

Categories should be chosen carefully since a bad choice can prejudice the outcome of an investigation. Every value should belong to one and only one category, and there should be no doubt as to which one.

Nominal Data

A set of data is said to be nominal if the values / observations belonging to it can be assigned a code in the form of a number where the numbers are simply labels. You can count but not order or measure nominal data. For example, in a data set males could be coded as 0, females as 1; marital status of an individual could be coded as Y if married, N if single.

Ordinal Data

A set of data is said to be ordinal if the values / observations belonging to it can be ranked (put in order) or have a rating scale attached. You can count and order, but not measure, ordinal data.

The categories for an ordinal set of data have a natural order, for example, suppose a group of people were asked to taste varieties of biscuit and classify each biscuit on a rating scale of 1 to 5, representing strongly dislike, dislike, neutral, like, strongly like. A rating of 5 indicates more enjoyment than a rating of 4, for example, so such data are ordinal.

However, the distinction between neighbouring points on the scale is not necessarily always the same. For instance, the difference in enjoyment expressed by giving a rating of 2 rather than 1 might be much less than the difference in enjoyment expressed by giving a rating of 4 rather than 3.

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Interval Scale

An interval scale is a scale of measurement where the distance between any two adjacents units of measurement (or 'intervals') is the same but the zero point is arbitrary. Scores on an interval scale can be added and subtracted but can not be meaningfully multiplied or divided. For example, the time interval between the starts of years 1981 and 1982 is the same as that between 1983 and 1984, namely 365 days. The zero point, year 1 AD, is arbitrary; time did not begin then. Other examples of interval scales include the heights of tides, and the measurement of longitude.

Continuous Data

A set of data is said to be continuous if the values / observations belonging to it may take on any value within a finite or infinite interval. You can count, order and measure continuous data. For example height, weight, temperature, the amount of sugar in an orange, the time required to run a mile.

Compare discrete data.

Frequency Table

A frequency table is a way of summarising a set of data. It is a record of how often each value (or set of values) of the variable in question occurs. It may be enhanced by the addition of percentages that fall into each category.

A frequency table is used to summarise categorical, nominal, and ordinal data. It may also be used to summarise continuous data once the data set has been divided up into sensible groups.

When we have more than one categorical variable in our data set, a frequency table is sometimes called a contingency table because the figures found in the rows are contingent upon (dependent upon) those found in the columns.

Example

Suppose that in thirty shots at a target, a marksman makes the following scores:

5 2 2 3 4 4 3 2 0 3 0 3 2 1 5455

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1 3 1 5 5 2 4 0 0 4 5 4 4 5 5

The frequencies of the different scores can be summarised as:

Score Frequency Frequency (%)

0 4 13%

1 3 10%

2 5 17%

3 5 17%

4 6 20%

5 7 23%

Pie Chart

A pie chart is a way of summarising a set of categorical data. It is a circle which is divided into segments. Each segment represents a particular category. The area of each segment is proportional to the number of cases in that category.

Example

Suppose that, in the last year a sports wear manufacturers has spent 6 million pounds on advertising their products; 3 million has been spent on television adverts, 2 million on sponsorship, 1 million on newspaper adverts, and a half million on posters. This spending can be summarised using a pie chart:

Bar Chart

A bar chart is a way of summarising a set of categorical data. It is often used in exploratory data analysis to illustrate the major features of the distribution of the data in a convenient form. It displays the data using a number of rectangles, of the same width, each of which represents a particular category. The length (and hence area) of each rectangle is proportional to the number of cases in the category it represents, for example, age group, religious affiliation.

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Bar charts are used to summarise nominal or ordinal data.

Bar charts can be displayed horizontally or vertically and they are usually drawn with a gap between the bars (rectangles), whereas the bars of a histogram are drawn immediately next to each other.

Dot Plot

A dot plot is a way of summarising data, often used in exploratory data analysis to illustrate the major features of the distribution of the data in a convenient form.

For nominal or ordinal data, a dot plot is similar to a bar chart, with the bars replaced by a series of dots. Each dot represents a fixed number of individuals. For continuous data, the dot plot is similar to a histogram, with the rectangles replaced by dots.

A dot plot can also help detect any unusual observations (outliers), or any gaps in the data set.

Histogram

A histogram is a way of summarising data that are measured on an interval scale (either discrete or continuous). It is often used in exploratory data analysis to illustrate the major features of the distribution of the data in a convenient form. It divides up the range of possible values in a data set into classes or groups. For each group, a rectangle is constructed with a base length equal to the range of values in that specific group, and an area proportional to the number of observations falling into that group. This means that the rectangles might be drawn of non-uniform height.

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The histogram is only appropriate for variables whose values are numerical and measured on an interval scale. It is generally used when dealing with large data sets (>100 observations), when stem and leaf plots become tedious to construct. A histogram can also help detect any unusual observations (outliers), or any gaps in the data set.

Compare bar chart.

Stem and Leaf Plot

A stem and leaf plot is a way of summarising a set of data measured on an interval scale. It is often used in exploratory data analysis to illustrate the major features of the distribution of the data in a convenient and easily drawn form.

A stem and leaf plot is similar to a histogram but is usually a more informative display for relatively small data sets (<100 data points). It provides a table as well as a picture of the data and from it we can

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readily write down the data in order of magnitude, which is useful for many statistical procedures, e.g.

in the skinfold thickness example below:

We can compare more than one data set by the use of multiple stem and leaf plots. By using a back-to-back stem and leaf plot, we are able to compare the same characteristic in two different groups, for example, pulse rate after exercise of smokers and non-smokers.

Box and Whisker Plot (or Boxplot)

A box and whisker plot is a way of summarising a set of data measured on an interval scale. It is often used in exploratory data analysis. It is a type of graph which is used to show the shape of the distribution, its central value, and variability. The picture produced consists of the most extreme values in the data set (maximum and minimum values), the lower and upper quartiles, and the median.

A box plot (as it is often called) is especially helpful for indicating whether a distribution is skewed and whether there are any unusual observations (outliers) in the data set.

Box and whisker plots are also very useful when large numbers of observations are involved and when two or more data sets are being compared.

See also 5-Number Summary.

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5-Number Summary

A 5-number summary is especially useful when we have so many data that it is sufficient to present a summary of the data rather than the whole data set. It consists of 5 values: the most extreme values in the data set (maximum and minimum values), the lower and upper quartiles, and the median.

A 5-number summary can be represented in a diagram known as a box and whisker plot. In cases where we have more than one data set to analyse, a 5-number summary is constructed for each, with corresponding multiple box and whisker plots.

Outlier

An outlier is an observation in a data set which is far removed in value from the others in the data set. It is an unusually large or an unusually small value compared to the others.

An outlier might be the result of an error in measurement, in which case it will distort the interpretation of the data, having undue influence on many summary statistics, for example, the mean.

If an outlier is a genuine result, it is important because it might indicate an extreme of behaviour of the process under study. For this reason, all outliers must be examined carefully before embarking on any formal analysis. Outliers should not routinely be removed without further justification.

Symmetry

Symmetry is implied when data values are distributed in the same way above and below the middle of the sample.

Symmetrical data sets:

a. are easily interpreted; b. allow a balanced attitude to outliers, that is, those above and below the

middle value ( median) can be considered by the same criteria; c. allow comparisons of spread or dispersion with similar data sets.

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Many standard statistical techniques are appropriate only for a symmetric distributional form. For this reason, attempts are often made to transform skew-symmetric data so that they become roughly symmetric.

Skewness

Skewness is defined as asymmetry in the distribution of the sample data values. Values on one side of the distribution tend to be further from the 'middle' than values on the other side.

For skewed data, the usual measures of location will give different values, for example, mode<median<mean would indicate positive (or right) skewness.

Positive (or right) skewness is more common than negative (or left) skewness.

If there is evidence of skewness in the data, we can apply transformations, for example, taking logarithms of positive skew data.

Compare symmetry.

Transformation to Normality

If there is evidence of marked non-normality then we may be able to remedy this by applying suitable transformations.

The more commonly used transformations which are appropriate for data which are skewed to the right with increasing strength (positive skew) are 1/x, log(x) and sqrt(x), where the x's are the data values.

The more commonly used transformations which are appropriate for data which are skewed to the left with increasing strength (negative skew) are squaring, cubing, and exp(x).

Scatter Plot

A scatterplot is a useful summary of a set of bivariate data (two variables), usually drawn before working out a linear correlation coefficient or fitting a regression line.

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It gives a good visual picture of the relationship between the two variables, and aids the interpretation of the correlation coefficient or regression model.

Each unit contributes one point to the scatterplot, on which points are plotted but not joined. The resulting pattern indicates the type and strength of the relationship between the two variables.

Illustrations

a. The more the points tend to cluster around a straight line, the stronger the linear relationship between the two variables (the higher the correlation).

b. If the line around which the points tends to cluster runs from lower left to upper right, the relationship between the two variables is positive (direct).

c. If the line around which the points tends to cluster runs from upper left to lower right, the relationship between the two variables is negative (inverse).

d. If there exists a random scatter of points, there is no relationship between the two variables (very low or zero correlation).

e. Very low or zero correlation could result from a non-linear relationship between the variables. If the relationship is in fact non-linear (points clustering around a curve, not a straight line), the correlation coefficient will not be a good measure of the strength.

A scatterplot will also show up a non-linear relationship between the two variables and whether or not there exist any outliers in the data.

More information can be added to a two-dimensional scatterplot - for example, we might label points with a code to indicate the level of a third variable.

If we are dealing with many variables in a data set, a way of presenting all possible scatter plots of two variables at a time is in a scatterplot matrix.

Sample Mean

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The sample mean is an estimator available for estimating the population mean . It is a

measure of location, commonly called the average, often symbolised .

Its value depends equally on all of the data which may include outliers. It may not appear representative of the central region for skewed data sets.

It is especially useful as being representative of the whole sample for use in subsequent calculations.

Example

Lets say our data set is: 5 3 54 93 83 22 17 19.

The sample mean is calculated by taking the sum of all the data values and dividing by the total number of data values:

See also expected value.

Median

The median is the value halfway through the ordered data set, below and above which there lies an equal number of data values.

It is generally a good descriptive measure of the location which works well for skewed data, or data with outliers.

The median is the 0.5 quantile.

Example

With an odd number of data values, for example 21, we have:

Data 96 48 27 72 39 70 7 68 99 36 95 4 6 13 34 74 65 42 28 54 69

Ordered Data 4 6 7 13 27 28 34 36 39 42 48 54 65 68 69 70 72 74 95 96 99

Median 48, leaving ten values below and ten values above

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With an even number of data values, for example 20, we have:

Data 57 55 85 24 33 49 94 2 8 51 71 30 91 6 47 50 65 43 41 7

Ordered Data

2 6 7 8 24 30 33 41 43 47 49 50 51 55 57 65 71 85 91 94

Median Halfway between the two 'middle' data points - in this case halfway between 47 and 49, and so the median is 48

Mode

The mode is the most frequently occurring value in a set of discrete data. There can be more than one mode if two or more values are equally common.

Example

Suppose the results of an end of term Statistics exam were distributed as follows:

Student: Score:</I.< td>

1 94

2 81

3 56

4 90

5 70

6 65

7 90

8 90

9 30

Then the mode (most common score) is 90, and the median (middle score) is 81.

Dispersion

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The data values in a sample are not all the same. This variation between values is called dispersion.

When the dispersion is large, the values are widely scattered; when it is small they are tightly clustered. The width of diagrams such as dot plots, box plots, stem and leaf plots is greater for samples with more dispersion and vice versa.

There are several measures of dispersion, the most common being the standard deviation. These measures indicate to what degree the individual observations of a data set are dispersed or 'spread out' around their mean.

In manufacturing or measurement, high precision is associated with low dispersion.

Range

The range of a sample (or a data set) is a measure of the spread or the dispersion of the observations. It is the difference between the largest and the smallest observed value of some quantitative characteristic and is very easy to calculate.

A great deal of information is ignored when computing the range since only the largest and the smallest data values are considered; the remaining data are ignored.

The range value of a data set is greatly influenced by the presence of just one unusually large or small value in the sample (outlier).

Examples

1. The range of 65,73,89,56,73,52,47 is 89-47 = 42. 2. If the highest score in a 1st year statistics exam was 98 and the lowest 48,

then the range would be 98-48 = 50.

Inter-Quartile Range (IQR)

The inter-quartile range is a measure of the spread of or dispersion within a data set.

It is calculated by taking the difference between the upper and the lower quartiles. For example:

Data 2 3 4 5 6 6 6 7 7 8 9

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Upper quartile 7

Lower quartile 4

IQR 7 - 4 = 3

The IQR is the width of an interval which contains the middle 50% of the sample, so it is smaller than the range and its value is less affected by outliers.

Quantile

Quantiles are a set of 'cut points' that divide a sample of data into groups containing (as far as possible) equal numbers of observations.

Examples of quantiles include quartile, quintile, percentile.

Percentile

Percentiles are values that divide a sample of data into one hundred groups containing (as far as possible) equal numbers of observations. For example, 30% of the data values lie below the 30th percentile.

See quantile. Compare quintile, quartile.

Quartile

Quartiles are values that divide a sample of data into four groups containing (as far as possible) equal numbers of observations.

A data set has three quartiles. References to quartiles often relate to just the outer two, the upper and the lower quartiles; the second quartile being equal to the median. The lower quartile is the data value a quarter way up through the ordered data set; the upper quartile is the data value a quarter way down through the ordered data set.

Example

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Data 6 47 49 15 43 41 7 39 43 41 36

Ordered Data 6 7 15 36 39 41 41 43 43 47 49

Median 41

Upper quartile 43

Lower quartile 15

See quantile. Compare percentile, quintile.

Quintile

Quintiles are values that divide a sample of data into five groups containing (as far as possible) equal numbers of observations.

See quantile. Compare quartile, percentile.

Sample Variance

Sample variance is a measure of the spread of or dispersion within a set of sample data.

The sample variance is the sum of the squared deviations from their average divided by one less than the number of observations in the data set. For example, for n observations x1, x2, x3, ... , xn with sample mean

the sample variance is given by

See also variance.

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Standard Deviation

Standard deviation is a measure of the spread or dispersion of a set of data.

It is calculated by taking the square root of the variance and is symbolised by s.d, or s. In other words

The more widely the values are spread out, the larger the standard deviation. For example, say we have two separate lists of exam results from a class of 30 students; one ranges from 31% to 98%, the other from 82% to 93%, then the standard deviation would be larger for the results of the first exam.

Coefficient of Variation

The coefficient of variation measures the spread of a set of data as a proportion of its mean. It is often expressed as a percentage.

It is the ratio of the sample standard deviation to the sample mean:

There is an equivalent definition for the coefficient of variation of a population, which is based on the expected value and the standard deviation of a random variable.


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2. Question # 2 of 10 ( Start time: 08:24:38 PM ) Total Marks: 1If f(x) is a continuous probability function, then P(X = 2) is:Select correct option: 1 0 1/2 2


4. Question # 4 of 10 ( Start time: 08:26:51 PM ) Total Marks: 1If A and B are mutually exclusive events with P (A) =0.25 and P (B) = 0.50, Then P (A or B) =………Select correct option: 0.25 0.75 0.50 1

Muhammad Rashid Chishti 3336721100

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8. Question # 8 of 10 ( Start time: 08:31:42 PM ) Total Marks: 1If Y=3X+5,then S.D of Y is equal to

470

Select correct option: 9 s.d(x) 3 s.d(x) s.d(x)+5 3s.d(x)+5


9. Question # 9 of 10 ( Start time: 08:33:16 PM ) Total Marks: 1The probability of drawing a red queen card from well-shuffled pack of 52 playing cards isSelect correct option: 4/52 2/52 13/52 26/52

10.Question # 10 of 10 ( Start time: 08:34:40 PM ) Total Marks: 1If P (B|A) = 0.25 and P (A and B) =0.20, then P (A) isSelect correct option: 0.05 0.80 0.95 0.75

11.Question # 1 of 10 ( Start time: 08:57:45 PM ) Total Marks: 1When a coin is tossed 3 times, the probability of getting 3 tails isSelect correct option: 1/8 3/8

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3/6 2/8


12.Question # 2 of 10 ( Start time: 08:59:14 PM ) Total Marks: 1In how many ways can a team of 11 players be chosen from a total of 16 players?Select correct option: 4368(not confirmed) 2426 5400 2680

13.Question # 3 of 10 ( Start time: 09:00:38 PM ) Total Marks: 1The standard deviation of c (constant) isSelect correct option: c c square 0 does not exist


14.Question # 4 of 10 ( Start time: 09:01:46 PM ) Total Marks: 1If P (E) is the probability that an event will occur, which of the following must be false:Select correct option: P(E)= - 1 P(E)=1

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P(E)=1/2 P(E)=1/3


15.Question # 5 of 10 ( Start time: 09:02:48 PM ) Total Marks: 1Let E and F be events associated with the same experiment. Suppose the E and F are independent and that P(E) = 1/4 and P(F) = 1/2 Then P(E U F) is:Select correct option: 1/8 3/4 7/8 5/8


16.Question # 6 of 10 ( Start time: 09:04:09 PM ) Total Marks: 1A student solved 25 questions from first 50 questions of a book to be solved. The probability that he will solve the remaining all questions is:Select correct option: 0.25 0.5 1 0

17.Question # 7 of 10 ( Start time: 09:05:31 PM ) Total Marks: 1If Y=bX, then variance of Y isSelect correct option: b*2 var(x) var(x)

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b var(x) b square root var(x)

18.Question # 9 of 10 ( Start time: 09:07:48 PM ) Total Marks: 1The classical definition of probability assumes:Select correct option: Exhaustive events Mutually exclusive events Equally likely evens Independent evens


19.Question # 10 of 10 ( Start time: 09:08:50 PM ) Total Marks: 1In scatter diagram, the variable plotted along Y-axis is:Select correct option: Independent variable Dependent variable Continuous variable Discrete variable

20.Which of the following measures of dispersion are based on deviations from the mean? Select correct option:


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All of the these


21.What does it mean when a data set has a standard deviation equal to zero? Select correct option:


22.A set of possible values that a random variable can assume and their associated probabilities of occurrence are referred to as ________. Select correct option:


23.Which of the following can never be probability of an event? Select correct option:

0 1 0.5 -0.5

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24.The standard deviation of -1, -1, -1, -1 will be Select correct option:



25.Which formula represents the probability of the complement of event A: Select correct option:

1 + P (A) 1 - P (A) P (A) P (A) -1

26.The Special Rule of Addition is used to combine: Select correct option:


27.set which is the sub-set of every set is Select correct option:

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28.E(4X + 5) =________ Select correct option:

12 E (X) 4 E (X) + 5 16 E (X) + 5 16 E (X)

29.When two dice are rolled the number of possible sample points is : Select correct option:

6 12 24 36

30.Question # 1 of 10 ( Start time: 09:43:04 PM ) Total Marks: 1 If two events A and B are not mutually exclusive then Select correct option:


P (A or B) = P (A) + P (B)

P (A or B) = P (A) x P (B)

477

P (A or B) = P (A) + P (B)

31.Question # 2 of 10 ( Start time: 09:43:59 PM ) Total Marks: 1 Evaluate (10-4)! Select correct option:

1000 720 480 32


32.Question # 3 of 10 ( Start time: 09:45:01 PM ) Total Marks: 1 When E is an impossible event, then P(E) is: Select correct option:

0 1 2 0.5

33.Question # 4 of 10 ( Start time: 09:46:20 PM ) Total Marks: 1 When we toss a coin , we get only: Select correct option:


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34.Question # 5 of 10 ( Start time: 09:47:15 PM ) Total Marks: 1 For exhaustive events, the P(AUBUC) is equal to: Select correct option:

P(A) P(S) P(A) * P(B)* P(C) P(B)


35.Question # 6 of 10 ( Start time: 09:48:21 PM ) Total Marks: 1 A student solved 25 questions from first 50 questions of a book to be solved. The probability that he will solve the remaining all questions is: Select correct option:

0.25 0.5 1 0

36.A set of possible values that a random variable can assume and their associated probabilities of occurrence are referred to as ________. Select correct option:


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37.Question # 9 of 10 ( Start time: 09:50:35 PM ) Total Marks: 1 If we roll a die then probability of getting a ‘6’ will be Select correct option:

2/6

1/6

4/6

1

38.Question # 10 of 10 ( Start time: 09:51:36 PM ) Total Marks: 1 If P(A) = 0.45, P(B) = 0.35, and P(A and B) = 0.25, then P(A | B) is: Select correct option:

1.4 1.8 0.714 0.556

39.Question # 8 of 10 ( Start time: 09:49:53 PM ) Total Marks: 1 Which of the following is not a measure of central tendency? Select correct option:

Percentile

480

Quartile

Standard deviation

Mode


40.Question # 1 of 10 ( Start time: 09:56:49 PM ) Total Marks: 1

Random experiment can be repeated any no. of times under the……… conditions. Select correct option:

Different Similar



What is the probability of sure event? Select correct option:

0 1 0.5 2



The simultaneous occurrence of two events is called: Select correct option:


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In regression analysis, the variable that is being predicted is the Select correct option:

Dependent variable



None of these

44.The probability of continuous random variable x on any particular point is

always zero..

Yes

No

45.P(an event) =no of favorable outcome/total no. of outcomes is the definition of

Subjective approach

Objective approach

46. If C is a constant ,then E(c)=

0

1

C

-c

47.Question # 6 of 10 482

When we toss a fair coin 4 times, the sample space consists of….points.

4

8

12

16

48.When a coin is tossed 3 times, the probability of getting 3 tails is

1/8

3/8

3/6

2/8

49.If we roll three fair dices then the total number of outcomes is:

6

36

216

1296

50.The probability of an event is always:

greater than 0

less than 1

between o and 1

greater than 1

51.For exhaustive events, the P(AUBUC) is equal to:

483

P(A)

P(S)

P * P(B)* P(C)

52.In a multiplication theorem P (A and B) equals:

P(A)

P (B) P(A) + P (B)

P(A) * P (B|A)

P(B\A)*P(B)

53.If a die is rolled, what is the probability of getting an even number greater

than 2?

1/2

1/3

2/3

5/6

54.In a Discrete probability distribution, P (x > 23) is read as:

P (there are more than 23 successes)

P (there are less than 23 successes)

P (there are at least 23 successes)

P (there are at most 23 successes)

55.When E is an impossible event, then P(E) is:

484

0

1

2

0.5

56.A dormitory on campus houses 200 students. 120 are male, 50 are upper

division students, and 40 are upper division male students.A student is selected at random. The probability of selecting a lower division student, given the student is a female, is:


7/8

7/20

7/15

¼

57.A discrete probability function f(x) is always:

Zero

One

Negative

Non-negative

58.The function F(x) gives the probability of the event that X takes a value ......

Less than x

Greater or equal to x

Less or equal x

Equal to x

485

59.Which of the following is not a measure of central tendency?

Percentile

Quartile

Standard deviation

Mode

60.When we toss a coin, we get only

1 outcome

2 outcome

3 outcome

4 outcome

61.In a simple regression line model ,it is assume that the intercept parameter is

equal to zero,

The regression line will pass through the origin.

The regression line will pass through the point (0,10)

The regression line will pass through the point (0,-10)

The slope of the line will also be zero.

62.If p(AnB)=p(A/B).p(B),then A and B are

Independent

Dependant

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Equally likely

Mutually exclusively

63.A fair coin is tossed three times, the probability that at least one head appears,

1/8

7/8

3/8

5/8


64.In probability distribution, the sum of probabilities is equals to

0

0.1

0.5

1


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www.pakfree.webs.com

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Mean

The mean of the sampling distribution (of the mean) is the

mean of the population from which the scores were

sampled.

Therefore, if a population has a mean, μ, then the

sampling distribution of the mean is also μ.

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mailto:[email protected]

The symbol is used to refer to the mean of the sampling

distribution of the mean.

Therefore, the formula for the mean of the sampling

distribution of the mean can be written as:

Variance

The variance of the sampling distribution of the mean is

computed as follows:

That is, the variance of the sampling distribution of the

mean is the population variance divided by N.

Thus, the larger the sample size, the smaller the variance

of the sampling distribution of the mean.

Population mean

Population mean is calculated from the population information (data). let we have a

population 2, 4, 6, 10. We have to find the mean of this population we proceed as

Second query, in this example all events have equal probability of occurrence 1/5.

No. of

Faulty Items

(X)

Probability

f(x)

x.f(x)

0 1/5 0

1 1/5 1/5

488

2 1/5 2/5

3 1/5 3/5

4 1/5 4/5

Total 1 10/5

We have drawn all possible samples of size 2 without replacement from population 0,

1, 2, 3, 4.

All possible sample with replacement =

After drawing sample (not given in the example), we have make the sampling

distribution of means that is given in the example. Then we have fine the mean of this

distribution which is 2.

It is property that sample mean is always equal to population mean i.e.

The formulas for standard deviation:

489

The value of constant e:

The ‘e’ is a constant and its value is 2.7183.

Putting this value, you can find out the expression using calculator.

OR

Uniform Distribution:

The Uniform distribution is defined by the function

The above function is a proper probability density function because of the fact that:

i) Since a < b, therefore f(x) > 0.

ii)

490

Hence its a proper probability density function.

Binomial Distribution (Lesson 28)

Definition:

The Binomial Distribution is one of the discrete probability distribution. It is used when there are exactly two mutually exclusive outcomes of a trial. These outcomes are appropriately labeled Success and Failure. The Binomial Distribution is used to obtain the probability of observing r successes in n trials, with the probability of success on a single trial denoted by p.

Formula

Where

n = the total no. of trials

p = probability of success in each trial

q = probability of failure in each trial (i.e. q = 1 - p)

x = no. of successes in n trials.

x = 0, 1, 2, … n

491

Example 1

Suppose a die is tossed 5 times. What is the probability of getting exactly 2 fours?

Solution: This is a binomial experiment in which the number of trials is equal to 5, the number of successes is equal to 2, and the probability of success on a single trial is 1/6 or about 0.167. Therefore, the binomial probability is:

b(2; 5, 0.167) = 5C2 * (0.167)2 * (0.833)3 b(2; 5, 0.167) = 0.161

Question No: 1 (Marks: 1) - Please choose one10! =………….

► 362880► 3628800► 362280► 362800

Question No: 2 (Marks: 1) - Please choose oneIf a player well shuffles the pack of 52 playing cards, then the probability of a black card from 52 playing cards is:

152

►13

52►

4

52►

26

52►

Question No: 3 (Marks: 1) - Please choose oneThe probability of drawing a ‘jack card ‘from 52 playing cards is:

► 1

524

52

492

►13

52►

26

52►

Question No: 4 (Marks: 1) - Please choose oneWhich dispersion is used to compare variation of two series?

► C.V.► Q.D.

493

► M.D.► S.D.

Question No: 5 (Marks: 1) - Please choose oneIf all the values fall on the same straight line and the line has a positive slope then what will be the value of the correlation coefficient ‘r’:

► 0 ≤ r ≤ 1► r ≥ 0► r = +1► r=-1

Question No: 6 (Marks: 1) - Please choose oneIn a regression line Y= a + bX, the value of the correlation coefficient will be zero if:

► Intercept a = 0► Intercept a ≠ 0► Slope b = 0► Slope b ≠ 0

Question No: 7 (Marks: 1) - Please choose oneWhen two coins are tossed the probability of at least one head is:

► 1/4► 3/4► 2/4► 4/4

Question No: 8 (Marks: 1) - Please choose oneWhich one of the following measurement does not divide a set of observations into equal parts?

► Quartiles► Deciles► Percentiles► Standard deviations

Question No: 9 (Marks: 1) - Please choose oneIn the model Y = mX + a, Y is also known as the:

► Predictor variable► Independent variable► Predicted (dependent) variable► Explanatory variable


494

According to empirical rule approximately 95% of the measurements will fall under which interval?

► X S

► X 2 S

► X 3S

► X 4S

Question No: 11 (Marks: 1) - Please choose oneWhich one of the following is written at the top of the table?

► Source note► Foot note► Prefatory note► Title

Question No: 12 (Marks: 1) - Please choose oneIf a curve has a longer tail to the right, it is called:

► Positively skewed► Negatively skewed► J-shaped► Symmetric

Question No: 13 (Marks: 1) - Please choose oneWhich one of the following is the class frequency?

► The number of observations in each class► The difference between consecutive lower class limits► Always contains at least 5 observations► Usually a multiple of the lower limit of the first class

Question No: 14 (Marks: 1) - Please choose onef ()x

If X is a discrete random variable, then the function is

► A probability function► A probability density function► A density function► A distribution function

Question No: 15 (Marks: 1) - Please choose oneWhich one of the following graphs is used for a time series data?

495

► Histogram► Historigram► Frequency curve► Frequency polygon



► Ogive► Frequency polygon► Frequency curve► Historigram

Question No: 17 (Marks: 1) - Please choose oneIf mean of the two observations is 10.5, then median of these two observations will be:

► 7.5► 8.5► 9.5► 10.5

Question No: 18 (Marks: 1) - Please choose oneWhich one is the formula of mid range?

xm x0►

x0 xm

►x0 xm

2►

x0 xm

► 2

Question No: 19 (Marks: 1) - Please choose oneWhich one of the following is not included in measures of central tendency?

► Quartile deviation► Harmonic mean► Geometric mean► Arithmetic mean

Question No: 20 (Marks: 1) - Please choose oneFor the given data 2, 3, 7, 0, -8 G. M will be:

► Negative

496

► Positive► Zero► Undefined

Question No: 21 (Marks: 2)Why measure of central tendency and measure of dispersion are complementary to

each other?

Answer: Together both measures give us adequate description of data.

Question No: 22 (Marks: 2)What do you know about discrete random variable?

Answer:Such a numerical quantity whose value is determined by the value of a random experiment is called a random variable.

Example: If we toss three dice together and let X represents the number of heads, then the random variable X consists of the value 0, 1, 2, and 3. the X in this example is a discrete random variable.

Question No: 23 (Marks: 3)What is the subjective approach to the probability?

Answer:Subjective probability is a measure of the strength of a person’s belief regarding the occurrence of an event A. Probability in this sense is purely subjective and is based on whatever evidence is available to the individual.

It has a disadvantage that two or more persons faced with the same evidence may arrive at different probabilities.

Example:

Suppose a panel of three judges is hearing a trial. It is possible that based on the evidence that is presented; two of them arrive at the conclusion that the accused is guilty while one of them decides that the evidence is not strong to draw this conclusion.

Question No: 24 (Marks: 3)Explain the difference between absolute dispersion and relative dispersion:

Answer:

Question No: 25 (Marks: 5)Differentiate between the mutually exclusive events and exhaustive events.

Answer:

497

Mutually Exclusive Events: Two events A and B of a single experiment are said to be mutually exclusive if and only if they both can’t occur at the same time.

Example:When a die is rolled, the events ‘even number’ and odd number are mutually exclusive as we can get either an even number or an odd number in one throw, not both at the same time.

Exhaustive Events: Events are said to be collectively exhaustive, when the union of mutually exclusive events is equal to the entire sample space S.

Examples:In the coin tossing experiment, head and tail are collectively exhaustive events.

Question No: 26 (Marks: 5)Find the first two moments about mean from the following data.

X= 34, 70, 42, 54, 40, 68, 56, 38, 36, 72

498

Sta 301 solved quizplz make sure all the answers are correct

Question # 1 of 10 ( Start time: 11:13:38 AM ) Total Marks: 1Which of the following statements about confidence intervals is inaccurate?Select correct option:If we keep the sample size ?xed, the con?dence inte A con?dence interval for a mean always contains the If we keep the con?dence coe?cient ?xed, the con?d If the population standard deviation increases, the c

Quiz Start Time: 11:13 AM Time Left 80sec(s)Question # 2 of 10 ( Start time: 11:14:06 AM ) Total Marks: 1Probability of type II error isSelect correct option:aB1-a1-B

Quiz Start Time: 11:13 AM Time Left 79sec(s)Question # 3 of 10 ( Start time: 11:14:31 AM ) Total Marks: 1

499

A random sample of n=25 values gives sample mean 83. Can this sample be regarded as drawn from a normal

500

population with μ= 80 and s= 7? In this question the alternative hypothesis will be: http://www.vustudents.netSelect correct option:H1: μ = 80H1: μ ? 80H1: μ > 80H1: μ <80

Quiz Start Time: 11:13 AM Time Left 72sec(s)Question # 4 of 10 ( Start time: 11:15:08 AM ) Total Marks: 1With increase in sample size, distribution tends to be a.......Select correct option:Meso kurtic Normal Bell shaped Above all

Quiz Start Time: 11:13 AM Time Left 88sec(s)Question # 5 of 10 ( Start time: 11:15:49 AM ) Total Marks: 1You have measured the systolic blood pressure of a random sample of22 employees of a company. A 95% con?denceinterval for the mean systolic blood pressure for the employees is computed to be (120,138). Which of the followingstatements gives a valid interpretation of this interval?Select correct option:About 95% of the sample of employees has a systoli About 95% of the employees in the

501

http://www.vustudents.net/

company have a If the sampling procedure were repeated many times

502

Quiz Start Time: 11:13 AM Time Left 82sec(s)Question # 6 of 10 ( Start time: 11:16:13 AM ) Total Marks: 1Assume that a population consists of 7 similar containers having the following weights (km): 9.8, 10.2, 10.4, 9.8, 10.0,10.2, 9.6 What is the second moment about mean?Select correct option: http://www.vustudents.net0.262 kg0.069kg0.521 kg0.313kg

Quiz Start Time: 11:13 AM Time Left 86sec(s)Question # 7 of 10 ( Start time: 11:16:35 AM ) Total Marks: 1How many numbers of parameter(s) are in t-distribution?Select correct option:0123

Quiz Start Time: 11:13 AM Time Left 88sec(s)Question # 8 of 10 ( Start time: 11:17:00 AM ) Total Marks: 1With increase in sample size, distribution tends to be a.......

9


Select correct option:Meso kurticNormalBell shapedAbove all

Quiz Start Time: 11:13 AM Time Left 87sec(s)Question # 9 of 10 ( Start time: 11:17:14 AM ) Total Marks: 1F-distribution is a…………….. distribution.Select correct option:Unimodel Bimodal DiscreteNegatively skewed

Quiz Start Time: 11:13 AM Time Left 86sec(s)Question # 10 of 10 ( Start time: 11:17:29 AM ) Total Marks: 1Which one of the following sampling methods would give unbiased results, if you need to find out the number ofpeople in your town liking vanilla or chocolate ice creams?Select correct option:Ask my neighborsRandomly select a few ice cream shops in town, andAsk my friendsAsk my classmates

10

Question # 1 of 10 ( Start time: 11:22:56 AM ) Total Marks: 1A standard deviation obtained from sampling distribution of sample statistics is known asSelect correct option:Sampling ErrorStandard error

Question # 2 of 10 ( Start time: 11:23:07 AM ) Total Marks: 1F- distribution tends to normality, ifSelect correct option:V1~8V2~8V1 and V2 ~8Sample size is large

plz tell the logic or link you have watched it

Time Left 88 sec(s)Question # 3 of 10 ( Start time: 11:23:14 AM ) Total Marks: 1Consistency of an estimator can be checked by comparingSelect correct option:Mean MSE VarianceStandard deviation

11

Time Left 88 sec(s)Question # 4 of 10 ( Start time: 11:23:22 AM ) Total Marks: 1A standardized estimate has mean and varianceSelect correct option:(1, 0) (0, 1) (μ, s2) (μ, s)

plz tell the logic or link you watched it

Time Left 89 sec(s)Question # 5 of 10 ( Start time: 11:23:31 AM ) Total Marks: 1A composite hypothesis comprises of ………Select correct option:EqualityNot equal toLess than/greater(b) and (c)

Time Left 89 sec(s)

Question # 6 of 10 ( Start time: 11:23:39 AM ) Total Marks: 1For a particular hypothesis test, a=0.05and B=0.05. The power of

12

test is equal to:Select correct option:0.140.900.950.25

Time Left 86 sec(s)Question # 7 of 10 ( Start time: 11:23:47 AM ) Total Marks: 1In a t-distributionSelect correct option:Mean=median=mode Mean>Median<Mode Median >Mean>Mode Media<Mode<Mean

Time Left 69 sec(s)Question # 8 of 10 ( Start time: 11:24:18 AM ) Total Marks: 1If we reject the null hypothesis, we might be makingSelect correct option:Type I errorType II errorA correct decisionUnpredictable

13

sec(s)Question # 9 of 10 ( Start time: 11:24:49 AM ) Total Marks: 1The Central Limit Theorem is important in Statistics because it allows us to use the normal distribution to makeinferences concerning the population mean:Select correct option:Provided that the population is normally distributed a Provided that the population is normally distributed ( Provided that the sample size is reasonably large (fo Provided that the population is normally distributed a

Question # 10 of 10 ( Start time: 11:25:08 AM ) Total Marks: 1Herbicide A has been used for years in order to kill a particular type of weed, but an experiment is to be conducted inorder to see whether a new herbicide, Herbicide B, is more effective than Herbicide A. Herbicide A will continue tobe used unless there is sufficient evidence that Herbicide B is more effective. The alternative hypothesis in thisproblem is thatSelect correct option:(1)Herbicide A is more effective than Herbicide B (2)Herbicide B is more effective than Herbicide A (3)Herbicide A is not more effective than Herbicide B (4)Herbicide B is not more effective than Herbicide A

STA301 Qezz no 1 http://www.vustudents.net Quiz Start Time: 05:01 PM Time Left 81sec(s)

14


Question # 1 of 10 ( Start time: 05:01:05 PM ) Total Marks: 1What type of data is collected in population census? Select correct option:Tw o Ty pes

Quiz Start Time: 05:01 PM Time Left 77 sec(s)

Question # 2 of 10 ( Start time: 05:04:05 PM ) Total Marks: 1The collection of all outcomes for an experiment is calledSelect correct option:

a s a m ple s p a ce the intersection of eventsjoint probability population


Question # 3 of 10 ( Start time: 05:04:51 PM ) Total Marks: 1Which of the graph is used for a time series data: Select correct option:

Frequency curve Frequency polygon Historigram

His tog ra m ( no t s ure)


Question # 4 of 10 ( Start time: 05:06:06 PM ) Total Marks: 1A histogram is consists of a set of adjacent rectangles whose bases are

15

marked off by:Select correct option: http://www.vustudents.net

Class boundariesClass limitsClass frequencyClass marksQuiz Start Time: 05:01 PM Time Left 72 sec(s)

Question # 5 of 10 ( Start time: 05:06:56 PM ) Total Marks: 1The value that has half of the observations above it and half the observations below it is known as:Select correct option:

Mean Median ModeStandard deviation


Question # 6 of 10 ( Start time: 05:07:24 PM ) Total Marks: 1The height of a student is 60 inches. This is an example of ...........? Select correct option:

Continuous data Qualitative data Categorical data Discrete data


16


sec(s)

Question # 7 of 10 ( Start time: 05:08:06 PM ) Total Marks: 1Range of the values -2,-3,-4,-3,-9,-2,-8,-1,0 isSelect correct option:

0-98

9


http://www.vustudents.netQuestion # 8 of 10 ( Start time: 05:09:26 PM ) Total Marks: 1If the both tails of the distribution are equal, then distribution is called: Select correct option:

J-shapedSymmetrical

Positively SkewedNegatively Skewed


Question # 9 of 10 ( Start time: 05:09:54 PM ) Total Marks: 1Ranking scale also include the properties of which scale? Select correct option:

Nominal scale

17


Interval scale Ratio scale All of these


Question # 10 of 10 ( Start time: 05:10:56 PM ) Total Marks: 1Range of the values -2.50,-3.70,-4.80,-3.10,-9.70,-2.20,-8.90,-1.60, 0.60 isSelect correct option:

10.0310 . 3 0 9.109.00

The following data shows the number of hours worked by 200 statistics students. Number of Hours Frequency 0 - 9 40 10 - 19 50 20 - 29 70 30 -39 40 What is its class interval?910115

18

19

Question No: 1 ( Marks: 1 ) - Please choose oneFor a positively skewed distribution m3 will be:

► Positive► Negative► Zero► 1

Question No: 2 ( Marks: 1 ) - Please choose oneWhen data is labeled to identify an attribute of element, the measurement scale is:

► Ordinal► Interval► Nominal► Ratio


Yˆ 5 2 XSuppose the estimated equation is

is slop of the line:

► 0► 2► -2► 5

has been calculated for a set of data. What


If P(B|A) = 0.25 andP()A0.20B , then P(A) is:

► 0.05

► 0.80

► 0.95

► 0.75

Question No: 5 ( Marks: 1 ) - Please choose oneWhich branch of statistics deals with the techniques that are used to organize, summarize, and present the data:

► Advance statistics► Probability statistics► Descriptive statistics► Inferential statistics

20

Question No: 6 ( Marks: 1 ) - Please choose oneIn a sample of 800 students in a university, 160, or 20%, are Business majors. Based on

the above information, the school's paper reported that "20% of all the students at the university are Business majors." This report is an example of :

► A sample► A population► Sstatistical inference► Descriptive statistics



► Finite Set

► Infinite Set► Universal Set

► No of these

Question No: 8 ( Marks: 1 ) - Please choose oneIf X and Y are independent, then Var(X-Y) is equal to:

Var ()X() Var Y►

Var ()X() Var Y►

Var ()X Y►► Zero

Question No: 9 ( Marks: 1 ) - Please choose oneWhich of the following is the class frequency


Question No: 10 ( Marks: 1 ) - Please choose oneHow to construct the class interval:

► Divide the class frequencies in half► Divide the class frequency by the number of observations► Find the difference between consecutive lower class limits► Count the number of observations in the class

Question No: 11 ( Marks: 1 ) - Please choose oneData in the Population Census Report is:

► Ungrouped data

► Secondary data

► Primary data

► Arrayed data

Question No: 12 ( Marks: 1 ) - Please choose oneWhat is the range of -2,-3,-5,-10 :

► -12

► 8► -8

► 2

Question No: 13 ( Marks: 1 ) - Please choose oneThe algebraic sum of deviations from mean is:

► Maximum► Minimum► Zero► Undefined

Question No: 14 ( Marks: 1 ) - Please choose oneThe sum of squares of deviations from mean is:

► Undefined► Zero► Maximum► Minimum

Question No: 15 ( Marks: 1 ) - Please choose oneStatistic is a numerical quantity, which is calculated from:

► Population► Sample► Data► Observations

Question No: 16 ( Marks: 1 ) - Please choose oneWhich of the following is not based on all the observations?

► Arithmetic Mean► Geometric Mean► Harmonic mean► Mode

Question No: 17 ( Marks: 1 )Elaborate the word dispersion.


Question No: 18 ( Marks: 1 ) Define population.


Question No: 19 ( Marks: 2 )What does mean by the independence of two events:


Question No: 20 ( Marks: 3 ) The reciprocal of the values are

0.012, 0.0235, 0.0135Calculate Harmonic Mean

Harmonic mean is 250.037

Question No: 21 ( Marks: 5 )The probability that a student passes mathematics is 2/3 and the probability that he

passes English is 4/9. If the probability of passing at least one course is 4/5, what is the probability that he will pass both courses?

Math=2/3English=4/9Least one passing probability= 4/5

Math + English =2/3+4/9=1.114/5+1.11

=1.911

Question No: 22 ( Marks: 10 )A pair of dice is thrown, then



A hit first B Hit first B hit Second A Hit Second Both Hit Equally Both didn't Hit





P (A) P (B)

P (A) + P (B) P

(A) * P (B|A)

P(B\A)*P(B)



1

1/2

1

-1/2



1/6

2/36

1/36

1/12



0.65

0.05

0.03

0.07

Twenty percent of the students in a class of 100 are planning to go to graduate school. The standard deviation of this binomi aldistribution is:


20

2

4

16



1

0

1/2

2



Less than one

Greater than one


Zero


E(4X + 5) =


12 E (X)

4 E (X) + 5

16 E (X) + 5

16 E (X)



Mean

Variance

Mean & variance




Binomial experiment



Poisson experiment

MIDTERM EXAMINATION Spring 2009STA301- Statistics and Probability (Session - 6) Time: 60 minMarks: 38Question No: 1 ( Marks: 1 ) - Please choose oneFor a positively skewed distribution m3 will be:

► Positive► Negative► Zero► 1

Question No: 2 ( Marks: 1 ) - Please choose oneWhen data is labeled to identify an attribute of element, the measurement scale

is:

► Ordinal► Interval► Nominal► Ratio


Suppose the estimated equation is has been calculated for a set of data. What is slop of the line:

► 0► 2► -2► 5


If P(B|A) = 0.25 and , then P(A) is:

► 0.05

► 0.80

► 0.95

► 0.75


Which branch of statistics deals with the techniques that are used to organize, summarize, and present the data:► Advance statistics► Probability statistics► Descriptive statistics► Inferential statistics

Question No: 6 ( Marks: 1 ) - Please choose oneIn a sample of 800 students in a university, 160, or 20%, are Business majors.

Based on the above information, the school's paper reported that "20% of all the students at the university are Business majors." This report is an example of :► A sample► A population► Sstatistical inference► Descriptive statistics



► Finite Set

► Infinite Set► Universal Set

► No of these

Question No: 8 ( Marks: 1 ) - Please choose oneIf X and Y are independent, then Var(X-Y) is equal to:

►

►

►► Zero

Question No: 9 ( Marks: 1 ) - Please choose oneWhich of the following is the class frequency


Question No: 10 ( Marks: 1 ) - Please choose oneHow to construct the class interval:

► Divide the class frequencies in half► Divide the class frequency by the number of observations► Find the difference between consecutive lower class limits► Count the number of observations in the class

Question No: 11 ( Marks: 1 ) - Please choose oneData in the Population Census Report is:

► Ungrouped data

► Secondary data

► Primary data

► Arrayed data

Question No: 12 ( Marks: 1 ) - Please choose oneWhat is the range of -2,-3,-5,-10 :

► -12

► 8► -8► 2

Question No: 13 ( Marks: 1 ) - Please choose oneThe algebraic sum of deviations from mean is:

► Maximum► Minimum► Zero► Undefined

Question No: 14 ( Marks: 1 ) - Please choose oneThe sum of squares of deviations from mean is:

► Undefined► Zero► Maximum► Minimum

Question No: 15 ( Marks: 1 ) - Please choose oneStatistic is a numerical quantity, which is calculated from:

► Population► Sample

► Data► Observations

Question No: 16 ( Marks: 1 ) - Please choose oneWhich of the following is not based on all the observations?

► Arithmetic Mean► Geometric Mean► Harmonic mean► Mode

Question No: 17 ( Marks: 1 )Elaborate the word dispersion.


Question No: 18 ( Marks: 1 ) Define population.


Question No: 19 ( Marks: 2 )What does mean by the independence of two events:


Question No: 20 ( Marks: 3 ) The reciprocal of the values are

0.012, 0.0235, 0.0135Calculate Harmonic MeanHarmonic mean is 250.037

Question No: 21 ( Marks: 5 )The probability that a student passes mathematics is 2/3 and the probability that

he passes English is 4/9. If the probability of passing at least one course is 4/5, what is the probability that he will pass both courses?

Math=2/3English=4/9Least one passing probability= 4/5

Math + English =2/3+4/9=1.114/5+1.11=1.911

Question No: 22 ( Marks: 10 ) A pair of dice is thrown, then



A hit firstB Hit firstB hit Second A Hit Second Both Hit Equally Both didn't Hit



MIDTERM FALL 2010M NAD E E N204@G M A I L . C OM Dated 08-12-2010 (1st session)

S T A 301 Question No: 1 (Marks: 1) - Please choose oneIf a player well shuffles the pack of 52 playing cards, then the probability of a black card from 52 playing cards is:

1

52►

13

52►

4

52►

26

52 ►

Question No: 2 (Marks: 1) - Please choose oneThe probability of drawing a ‘jack card ‘from 52 playing cards is:

► 1

524

52 ►

13

52►

26

52►

Question No: 3 (Marks: 1) - Please choose oneIn a regression line Y= a + bX, the value of the correlation coefficient will be zero if: ► I n terce p t a = 0

► Intercept a ≠ 0► Slope b = 0► Slope b ≠ 0

Question No: 4 (Marks: 1) - Please choose oneWhich one of the following measurement does not divide a set of observations into equalparts?

► Quartiles► Deciles► Percentiles

► S ta nd ard d ev i at i o n s

mailto:[email protected]

Question No: 5 (Marks: 1) - Please choose oneWhich one of the following graphs is used for a time series data? ► Hi stogram

► Historigram► Frequency curve► Frequency polygon

Question No: 6 (Marks: 1) - Please choose oneIf you connect the mid-points of rectangles in a histogram by a series of lines that also touches the x-axis from both ends, what will you get?

► Ogive ► F re qu e n cy p o l ygon

► Frequency curve► Historigram

Question No:7 (Marks: 1) - Please choose oneWhich one is equal to explained variation divided by total variation?

• Sum of square due to regression• Coefficient of determinant• Standard error estimate• Coefficient of correlation (not confirmed)

Question No: 8 (Marks: 1) - Please choose onein the given series 1,2,1,1,2,2,2,3,4,5,3,2,3,1,4,2,3 mode of given is

• 43

• 3

12

•3

2

11

• 3 (n ot con f i rmed )

2*

Question No: 9 (Marks: 1) - Please choose oneTrue for the population,

• it must be large number of values• It must refer to people• It is collection of individual objects or measurement not confirmed)• It is the small part of whole

Question No:10 (Marks: 1) - Please choose oneData arrangement in ascending or descending order

• Array d ata• Group data• Ungroup data• Raw data

Question No: 11 (Marks: 1) - Please choose oneWhat is the main objective of Descriptive statistics?

• To test population properties

• To describe the data we collected• To infer something about the population• Makin g esti mate

Question No: 12 (Marks: 1) - Please choose oneWhich measure of central tendency?

• Variation of distribution• Average of di stribu ti on• Scattering of distribution• Dispersion of distribution

Question No: 13 (Marks: 1) - Please choose oneIf a=4 b=2 estimate line (i.e y=a+bx) and independent veriable has value 3 the the value of dependent veriable

• 6• 9• 10• 11

Question No: 14 (Marks: 1) - Please choose oneThe number of ways in which 4 books can be arranged

• 4• 6• 12• 24

Question No: 15 (Marks: 1) - Please choose oneIf we plot paired observed (x,y)=1…….n on graph is called,

• Polygon• Freasito diagram• Scatter diagram• Cumulative frequency diagram

Question No: 16 (Marks: 1) - Please choose oneThe simultaneous occurrence of two events is called

• Descriptive probability• Subjective probability not confirmed• Conditional probability• Joint probability

Question No: 17 (Marks: 1) - Please choose oneWhich one is the not measure of dispersion.

• The range• 50th percentile• Inter quartile range• Variance not confirmed

Question No: 18 (Marks: 1) - Please choose oneIn positively skew cure which relation is

• The mean, median and mode are equal• Mean is greater then median not confirmed• Median is greater then mean• Standard deviation must be greater then mean or median

Question No: 19 (Marks: 1) - Please choose oneWhen coin tossed we get only

1 o u tc o m e 2 outcomes3 outcomes4 outcomesQuestion No: 20 (Marks: 1) - Please choose one

When mean is 25 and S.D is 5 then CV is• 100%• 25%• 20% not confirmed• 10%

Question No: 21 (Marks: 2) - Please choose oneDefine rule for permutationQuestion No: 22 (Marks: 2) - Please choose one

If mean x=0.645 and S2 =0.215Then calculate coefficient of variationQuestion No: 23 (Marks: 3) - Please choose one

Find the probability of drawing white ball from bag out of 4 red, 8 blue and 3 white balls.Question No: 24 (Marks: 3) - Please choose one

If the equation of the least square regression line are y=2.64+0.648 andX=-1.91+0.917xFind coefficient of r.Question No: 25 (Marks: 5) - Please choose one

A and B are two independent events, ifP(A)=0.40, P(B)=0.30Find Probabilities i) P (A∩B)ii) P(A’∩B’Question No: 26 (Marks: 5) - Please choose one

If S={1,2,3,4,5,6,7,8,9,10} AndA={1,2,3,4} , B= {3,4,5,6} Prove that( A ∪ B) = ( A ∩ B)

STA301 Qezz no 1

Quiz Start Time: 05:01 PM Time Left 81sec(s)Question # 1 of 10 ( Start time: 05:01:05 PM ) Total Marks: 1What type of data is collected in population census? Select correct option:Two Types


Question # 2 of 10 ( Start time: 05:04:05 PM ) Total Marks: 1The collection of all outcomes for an experiment is calledSelect correct option:

a sample spacethe intersection of eventsjoint probability population


Question # 3 of 10 ( Start time: 05:04:51 PM ) Total Marks: 1Which of the graph is used for a time series data: http://www.vustudents.netSelect correct option:

Frequency curve Frequency polygon Historigram Histogram ( not sure)


Question # 4 of 10 ( Start time: 05:06:06 PM ) Total Marks: 1A histogram is consists of a set of adjacent rectangles whose bases are marked off by: Select correct option:

Class boundariesClass limitsClass frequency


Class marksQuiz Start Time: 05:01 PM Time Left 72 sec(s)

Question # 5 of 10 ( Start time: 05:06:56 PM ) Total Marks: 1The value that has half of the observations above it and half the observations below it is known as: http://www.vustudents.netSelect correct option:

Mean Median ModeStandard deviation


Question # 6 of 10 ( Start time: 05:07:24 PM ) Total Marks: 1The height of a student is 60 inches. This is an example of ...........? Select correct option: http://www.vustudents.net

Continuous data Qualitative data Categorical data Discrete data


Question # 7 of 10 ( Start time: 05:08:06 PM ) Total Marks: 1Range of the values -2,-3,-4,-3,-9,-2,-8,-1,0 isSelect correct option:

0-989





If the both tails of the distribution are equal, then distribution is called: Select correct option: http://www.vustudents.net

J-shapedSymmetrical

Positively SkewedNegatively Skewed


Question # 9 of 10 ( Start time: 05:09:54 PM ) Total Marks: 1Ranking scale also include the properties of which scale? Select correct option:

Nominal scale Interval scale Ratio scaleAll of these


Question # 10 of 10 ( Start time: 05:10:56 PM ) Total Marks: 1Range of the values -2.50,-3.70,-4.80,-3.10,-9.70,-2.20,-8.90,-1.60, 0.60 isSelect correct option:

10.0310.309.109.00
