Sampling for Research Simple Random Sampling

x Sampling Distribution ofSampling Distribution of Introduction to Sampling DistributionsIntroduction to Sampling Distributions Point EstimationPoint Estimation Simple Random SamplingSimple Random Sampling

Statistical InferenceStatistical Inference

1. A 1. A populationpopulation is the set of all the is the set of all the elements of interest Eg- Mobile elements of interest Eg- Mobile Phone usersPhone users

2. A 2. A samplesample is a subset of the population is a subset of the population

Eg- SAMSUNG mobile phone usersEg- SAMSUNG mobile phone users

1 . Finite populations are often you know the population:

• Organization membership roster• Credit card account numbers• Inventory product numbers

2. A 2. A simple random sample of size simple random sample of size nn from a from a finitefinite population of size population of size NN..

Also you can say n/N x 100

1. Infinite populations are often defined by an ongoing process whereby the elements of the population consist of items generated as though the process would operate indefinitely.

2. A 2. A simple random sample from an infinite populationsimple random sample from an infinite population is a sample selected such that the following conditionsis a sample selected such that the following conditions are satisfied.are satisfied.

• Each element selected comes from the sameEach element selected comes from the same population.population.• Each element is selected independently.Each element is selected independently.

2. The random number selection procedure cannot be2. The random number selection procedure cannot be used for infinite populations.used for infinite populations.

1. In the case of infinite populations, it is impossible to1. In the case of infinite populations, it is impossible to obtain a list of all elements in the population.obtain a list of all elements in the population.

Point EstimationPoint Estimation

x

1. In 1. In point estimationpoint estimation we use the data from the sample we use the data from the sample to compute a value of a sample statistic that servesto compute a value of a sample statistic that serves as an estimate of a population parameter.as an estimate of a population parameter.

2. We refer to 2. We refer to as the as the point estimatorpoint estimator of the of the populationpopulation mean mean ..

3. s3. s is the is the point estimatorpoint estimator of the population of the population standardstandard deviation deviation ..

4. p is the 4. p is the point estimatorpoint estimator of the population proportion of the population proportion pp..

Sampling ErrorSampling Error The sampling errors are:The sampling errors are:

| |p p2. For sample proportion2. For sample proportion

| |s 3. for sample standard deviation3. for sample standard deviation

| |x 1. For sample mean1. For sample mean

900 applications annually fromprospective students. Theapplication form contains a variety of informationincluding the individual’saptitude test score and whether or notthe individual desires on-campus housing.

The admissions would like to know thefollowing information:• the average score for the 900 applicants, and• the proportion of

applicants that want to live on campus.

You can do as follows.

1Conducting a census of the entire 900 applicants

2. Selecting a sample of 30 applicants

990900ix

2( ) 80900ix

648 .72900p

1.Mean Score1.Mean Score

2.Population Standard Deviation for SAT Score2.Population Standard Deviation for SAT Score

3.Population Proportion Wanting On-Campus 3.Population Proportion Wanting On-Campus HousingHousing

A Sample of 30 Applicants• Because the finite population has 900 elements, weBecause the finite population has 900 elements, we will need 3-digit random numbers to randomlywill need 3-digit random numbers to randomly select applicants numbered from 1 to 900.select applicants numbered from 1 to 900.

Taking a Sample of 30 ApplicantsTaking a Sample of 30 Applicants

•The you can select 30 students for the sample.The you can select 30 students for the sample.

• For example, Excel’s functionFor example, Excel’s function = RANDBETWEEN(1,900)= RANDBETWEEN(1,900) can be used to generate random numbers betweencan be used to generate random numbers between 1 and 900.1 and 900.

Simple Random Sampling: Using EXELSimple Random Sampling: Using EXEL

1. as Point Estimator of 1. as Point Estimator of x

3. as Point Estimator of 3. as Point Estimator of ppp

29,910 99730ix

xn

2( ) 163,996 75.21 29ix x

sn

20 30 .68p

2. s2. s as Point Estimator of as Point Estimator of

The The sampling distribution of sampling distribution of is the probability is the probabilitydistribution of all possible values of the sample distribution of all possible values of the sample mean .mean .

x

x

Sampling Distribution of Sampling Distribution of x

where: where: = the population mean= the population mean

EE( ) = ( ) = x

xExpected Value ofExpected Value of

Sampling Distribution of Sampling Distribution of x

1.Finite Population1.Finite Population 2. Infinite 2. Infinite PopulationPopulation

x n

N nN

( )1

x n

• is referred to as the is referred to as the standard standard error of theerror of the meanmean..

x

• A finite population is treated as beingA finite population is treated as being infinite if infinite if nn//NN << .05. .05.

• is the finite correction factor.is the finite correction factor.( ) / ( )N n N 1

xStandard Deviation ofStandard Deviation of