(1) Recommend the steps that should be taken to draw the particular sample described below. In addition, critically analyze the sampling plan.

a.   A stratified sample of 75 doctors, 75 lawyers, and 75 engineers who belong to a professional organization that you belong to.

b.   A simple random sample of 150 subscribers to your local newspaper.

c.    A systematic sample of 250 from a subscriber list of a trade publication.

(2) Download the G*Power software provided, and then use the software to submit the following:

    a. Calculate the sample size needed when given these factors:

·        one-tailed t-test with two independent groups of equal size

·        small effect size (see Piasta, S.B., & Justice, L.M., 2010)

·        alpha =.05

·        beta = .2

·        Assume that the result is a sample size beyond what you can obtain. Use the compromise function to compute alpha and beta for a sample half the size. Indicate the resulting alpha and beta. Analyze the result and decide if the study should be conducted with a smaller sample size. Explain your rationale. If the study is not worth doing with the smaller sample, discuss possible tradeoffs that may make the sample size feasible for your study.

b. Calculate the sample size needed when given these factors:

·        small effect size

·        alpha =.05

·        beta = .2

·        3 groups

·        Assume that ANOVA (fixed effects, omnibus, one-way)

   the result is a sample size beyond what you can obtain. Use the compromise function to compute alpha and beta for a sample approximately half the size. Give your rationale for your selected beta/alpha ratio. Indicate the resulting alpha and beta. Give an argument that your study is worth doing with the smaller sample.

(3) Describe the sampling method that would be appropriate for your intended research. Be sure to include the specification of the population, what would be used as a sampling frame, the method, and the procedure that you would use to draw the actual sample.

(1)(A)

(i)

A stratified sample of 75 doctors, 75 lawyers, and 75 engineers who belong to a professional organization that you belong to.:

Let N be the total number of people in the professional organization that you belong to.

 

Let

n1 = the total number of doctors in the professional organization that you belong to.

 

n2 = the total number of lawyers in the professional organization that you belong to.

 

n3 = the total number of engineers in the professional organization that you belong to.

 

so that

N = n1 + n2 + n3

 

Through Simple Random Sample technique,

select 75 doctors from n1 doctors.

select 75 lawyers from n2 lawyers.

select 75 engineers from n3 engineers.

 

In this way, we take a stratified sample of 75 doctors, 75 lawyers, and 75 engineers who belong to a professional organization that you belong to.

 

(ii)

Critical analysis of the stratified sampling plan.

Stratified Random Sampling allows the researcher to obtain a sample that best represents the entire population by dividing the population into homogeneous groups called strata: here: Doctors, Lawyers and Engineers.It is different from Simple Random Sampling because in the case of Simple Random Sampling, each possible sample is equally likely to occur, whereas in the case of Stratified Random Sampling, sampling is done from each stratum.

 

(B)

A simple random sample of 150 subscribers to your local newspaper.

(i)

Let

N = Total number of subscribers to your local newspaper.

To select 150 subscribers through Simple Random Sampling method, the following procedure is adopted.

Step 1:

Give serial numbers to each of the N subscribers from 1 to N.

Step 2:

Using Random Number Generator Software, obtain 150 random numbers out of the total number of N numbers.

Thus, we get a simple random sample of 150 subscribers to your local newspaper.

 

(ii)

Critical analysis of the Simple Random Sampling plan.

In Simple Random Sampling plan, every item in the population has the same likelihood of being selected in the sample. The selection of items completely depends on chance.

 

(C)

A systematic sample of 250 from a subscriber list of a trade publication.

(i)

Step 1:

Let

N = Total number of subscribers of a trade publication

Step 2:

Give serial numbers to each of the N subscribers from 1 to N.

Step 3:

Start with a random starting point

Step 4:

Select sample with a fixed, periodic sampling interval.

Step 5:

Stop the selection when we reach 250 subscribers for the sample.

Thus, we get a systematic sample of 250 from a subscriber list of a trade publication.

 

(ii)

Critical analysis of the Systematic Sampling plan.

Systematic Sampling plan eliminates phenomenon of clustered selection and has a low probability of contaminating the data.

 

 

(2)

By using G*Power3, we get the sample size

 

t tests - Means: Difference between two independent means (two groups)

 

Analysis:  A priori: Compute required sample size

 

Input:  Tail(s)  =  One

  Effect size d  =  0.2

  α err prob  =  0.05

  Power (1-β err prob)  =  0.8

  Allocation ratio N2/N1  =  1

 

Output:  Noncentrality parameter δ  =  2.489980

  Critical t  =  1.647323

  Df  =  618

  Sample size group 1  =  310

  Sample size group 2  =  310

  Total sample size  =  620

  Actual power  =  0.800218

 

2.

F tests - ANOVA: Fixed effects, omnibus, one-way

Analysis:  A priori: Compute required sample size

Input:  Effect size f  =  0.10

  α err prob  =  0.05

  Power (1-β err prob)  =  0.8

  Number of groups  =  3

Output:  Noncentrality parameter λ  =  9.690000

  Critical F  =  3.005042

  Numerator df  =  2

  Denominator df  =  966

  Total sample size  =  969

  Actual power  =  0.801101

 

(3)

Research relation between leadership style and employee commitment in organizations.

 

Technique- organizations with different leadership styles should be randomly selected and the employee's commitment should be recorded on the basis of their performance at the project on which they are working currently.

[Performance should be recorded on the scale of 1-10]

 

Sampling frame - list of all the employees of the organization will consider as a sampling frame.