Bioestadistica Problemario FINAL (1)

8/16/2019 Bioestadistica Problemario FINAL (1)

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TRUE FALSE QUESTIONS

1. The best point estimate for the population mean μ is the sample mean x. True

2. As the length of a confidence interval increases, the degree of confidence in its actuallycontaining the population parameter being estimated also increases. True

3. If the length of a confidence interval is very large, then the corresponding prediction is verymeaningful. False

4. La distribución correspondiente a en un nivel de confian!a del "#$ es de 1."%&. False

'. (l intervalo de confian!a para la media poblacional ) se puede calcular a partir de *+ -2-n donde es la desviación est/ndar de la población y n es el tama0o de la muestra. True

%. or a fixed confidence level, hen the sample si!e increases, the length of the confidenceinterval for a population mean decreases. False

3. or a fixed confidence level, hen the simple si!e decreases, the length of the confidenceinterval for a population mean decreases. True

#. The distribution of sample proportions is approximately normal provided that the sample si!en456. True

16. 7n intervalo de confian!a del "6$ para una media de la población, implica 8ue hay unaprobabilidad de 6,"6 de 8ue la población media este contenida en el intervalo de confian!a.True

11. A "6$ intervalo de confian!a para un par/metro de población significa 8ue si un n9mero largode intervalos de confian!a fueron construidos por muestras repetidas, a continuación enpromedio, "6$ de estos intervalos contendr:an el par/metro real. True

12. The point estimate of a population parameter is al ays at the center of the confidence intervalfor the parameter. False

15. ;hen repeated samples are selected from population, the point estimate for a given parameter ill al ays be the same value. True

14. The larger the level of confidence, the shorter the confidence interval. True

15. La men un estimado de la desviación de población est/ndar o la desviación est/ndar delmismo. False

13. In order to determine the sample si!e hen determining the population proportion, it isnecessary to ?no the level of confidence, the margin of error, and an estimate of thepopulation mean. True

18. The maximum error estimate gives a measure of accuracy hen computing the sample si!ere8uired to ma?e differences. False

19. @ased on the entral Limit Theorem for the difference of t o population proportion, e canassume, for large enough sample si!es, that the sampling distribution for the differencebet een t o sample proportions is exactly normally distributed. True

20. In computing e8ual simple si!es hen considering confidence intervals for the differencebet een t o population proportions, the simple si!e ill increase hen the margin of error isdecreased and the significance level is held fixed. False

21. ;hen computing largeBsample confidence intervals for the difference bet een t o population


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selected from this population ith a mean of %.2ft, "6$ confidence interval for the mean heightof these bas?etball players isbJ '.53# to 3.622 ft

GigmaH 2, nH1%, mediaH %.2, alfa-2 H 6.6', ! 6."'JH 1.%D'26. A ""$ confidence interval is to be constructed for a population mean from a random sample of

si!e 22. If the population standard deviation is ?no n , the table value to be used in thecomputation isbJ 2.556

21. The most common confidence levels and the corresponding ! values are listed belo . ;hichcorresponding ! value is incorrectaJ ""$, ! value H1.2#6

22. The heights in inchesJ of the students on a campus are assumed to have a normal distributionith a standard deviation of D in. A random sample of D" students as ta?en and yielded a

mean of %# in. The "'$ confidence interval for the population mean y isbJ %%.## to %".12 in

25. The length of time it ta?es a car salesperson to close a deal on a car sale is assumed to benormally distributed. A random sample of 166 such times as selected and yielded a mean of

5 h and variance of 56 min. The "#$ confidence interval for the mean length of time it ta?es acar salesperson to sell a car is

cJ 2.#5'2 to 5.1%D# h

23. The heights in inchesJ of the students on a campus are assumed to have a normal distributionith a variance of 2' in. Guppose that e ant to construct a "'$ confidence interval for the

population mean p and have it accurate to ithin 6.' in. The minimum sample si!e re8uired isbJ 2%"

5D. A researcher ishes to investigate the difference bet een the mean scores on a standardi!edtest for students ho ere exposed to t o different methods of teaching. Oo large a sampleshould the researcher ta?e e8ual sample si!e for each methodJ to be "" $ certain of ?no ing thedifference of the average scores to be ithin ± 5 points if the standard deviations for thepopulations are ' and #

aJ %%

5'. In 1"35, the Kraduate Pivision at the 7niversity of alifornia, @er?eley, did an observationalstudy on sex bias in admissions to the graduate school. It as found that in a particular ma


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5#. A researcher ants to determinate the difference bet een the proportions of males andfemales ho do volunteer or?. If a margin of error of ± 6.62 is acceptable at the "6 $ confidencelevel, hat is the maximum sample si!e that should be ta?en

aJ 5,5#5

FURT!ER E%ERCISES%. The TR( L scores for international students from t o different countries ere studied. Theinformation is given belo . onstruct a "6 $ confidence interval for the diference in the averagescores for the t o countries.

C&u#'r( 1 C&u#'r( 2 ́x1 = 490 ´ x2 = 462

s 1 = 80 s2 = 85

n1 = 110 n2 = 120

TRUE FALSE QUESTIONS1. A claim or statement about a population parameter is classified as the null hypothesis. True

2. A statement contradicting the claim in the null hypothesis about a population parameter isclassified as the alternative hypothesis. True

3. If e ant to claim that a population parameter is different from a specified value, this situationcan be considered as a oneBtailed test. True

D. The null hypothesis is considered correct until proved other ise. False

'. The type I error is the error e ma?e hen e fail to re


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and σ 12

and σ 22

are the respective variances, if the samples si!es are both greater than or

e8ual to 56 False

1'. In testing for the difference of t o population means, if the population variances are un?no nand the samples si!es from the populations are both greater than or e8ual to 56, the associatedtest statistic is approximately a ! score. True

13. If the null hypothesis is re


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1%. The number that separates the re


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bJ failing to re


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dJ re


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16. The level of significance can be any


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cJ value bet een 6 and 1, inclusive.11. If you fail to re


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dJ there si insufficient evidence to claim that the alternative hypothesis is true


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cJ ! W ! -215. ;ich of the follo ing general guidelines is used hen using the S value to perform hypothesistestdJ all the above1D. ;hen the S value is used in testing a hypothesis, e ill not re


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dJ OoV = 4 1'6,666 vs. O aV = Z 1'6,666


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bJ OoV = 4 %" vs. OaV = Z %"13. An advertisement on the TM claims that a certain brand of tire has an average lifetime of'6,666 miles. Guppose you plan to test this claim by ta?ing a sample of tires and putting them ontest. The correct set of hypotheses to set up is


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cJ OoV = H '6,666 vs. O aV = ] '6,6661#. The local ne spaper reported that at least 2'$ of a population in a university community

or?s at the university. )ou believe that the proportion is lo er. If you selected a random sample totest this claim, the appropriate set of hypotheses ould be


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dJ OoV = ] 6.2' vs. O aV = H 6.2'


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1". The local ne spaper claims that 1'$ of the residents of the community play the state lottery.If you plan to teste the claim by ta?ing a random sample from the community, the appropriate set of hypotheses is


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cJ OoV = H 6.1' vs. O aV = ] 6.1'26. The local ne spaper claims that no more than '$ of the residents of the community are on

elfare. If you plan to test the claim by ta?ing a random sample from the community, theappropriate set of hypotheses is


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a O oV = ^ 6.6' vs. O aV = W 6.6'21. or the follo ing information


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nH 1%=H 1'xH 1%

2H 1%


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bJ S valueH 6.1'#325. If you are performing a rightBtailed test for a single population mean, then you


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bJ ill not re


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a ill re


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cJ ill al ays re


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a ill al ays re


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cJ less than B1.%D'2#. It as reported that a certain population had a mean of 23. To test this claim, you selected arandom sample of si!e 166. The computed sample mean and sample standard deviation ere 2'and 3, respectively. The appropriate set of hypothesis for this test is


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dJ OoV = H 23 vs. OaV = ] 232". It as reported that a certain population had a mean of 23. To test this claim, you selected arandom sample of si!e 166. The computed sample mean and sample standard deviation ere 2'and 3, respectively. The computed test statistic for the appropriate set of hypotheses is


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dJ B2.#'31


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56. It as reported that a certain population had a mean of 23. To test this claim, you selected arandom sample of si!e 166. The computed sample mean and sample standard deviation ere 2'and 3, respectively. The S value for the appropriate set of Oypotheses is


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eJ 6.66D251. It as reported that a certain population had a mean of 23. To test this claim, you selected arandom sample of si!e 166. The computed sample mean and sample standard deviation ere 2'and 3, respectively. At the 6.6' level of significance, you can claim that the average of thispopulation is


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cJ Qot e8ual to 2353. If t o large samples selected independently fromt o different populations, the samplingdistribution of the difference of the samples meanscJ Oas a distribution that is approximately normal5#. If e are trying to establish that the mean of population 1 is greater than the mean ofpopulation 2, the appropriate set of hypothesis is


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fJ OoV =1 B=2 ^ 6 vs. O aV =1 B=2 W 6


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5". If e are trying to establish that the mean of population 1 is not the same as the mean of population 2, theappropriate set of hypothesis isbJ OoV =1 B=2 H 6 vs. O aV =1 B=2 ] 6D1. T o machines are used to fill '6Blb bags of dog food. Gample information for these t o machines is givenin the table.

`chine 1 `achine 2Gample si!e #1 %DGample mean poundsJ '1 D#Gample variance 1% 12The point estimate for the difference bet een the t o population means = 1 B=2J isbJ 5D2. The standard deviation standard errorJ for the distributioin of differences of sample means = 1 B=2J isaJ 6.%26'D5. If you are to conduct a test to determine hether the average amount dispensed by machine 1 issignificantly more than the average amount dispensed by machine 2, the appropriate set of hypotheses isdJ OoV =1 B=2 ≤ 6 vs. O aV =1 B=2 ¿ 6DD. D5. If you are to conduct a test to determine hether the average amount dispensed by machine 1 issignificantly more than the average amount dispensed by machine 2, the computed test statistic for this test iscJ D.#5D#D'. D5. If you are to conduct a test to determine hether the average amount dispensed by machine 1 issignificantly more than the average amount dispensed by machine 2, the appropriate set of hypotheses isbJ approximately 6,6D%. If you are to conduct a test at the 6.61 significance leve to determine hether the average amountdispensed by machine 1 is significantly more than the average amount dispensed by machine 2, the correctdecision isbJ re


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26B If the final averages from the semesters 1 and 2 are assumed to be normally distributed ith e8ualvariances, an appropriate range for the p value for the appropiate test isVcJ 6.2Z p Z 6.521B If the final averages from the semesters 1 and 2 are assumed to be normally distributed ith e8ualvariances, the correct decision for the appropriate test at a 6.6' level of significance hen the populationvariances are assumed to be e8ual isV

aJ do not re

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Bioestadistica Problemario FINAL (1)