A researcher wants to take a simple random sample of about 5% of the student bod

Question

A researcher wants to take a simple random sample of about 5% of the student body at each of two schools. The university has approximately 20,000 students, and the college has about 5000 students. Identify each of the following as true or false and justify your answer.

(a) The sampling variability is the same for both schools.

True. The sample sizes are different.

True. The sample sizes are the same.   

False. The sample sizes are different.

False. The sample sizes are the same.

(b) The sampling variability for the university is higher than that for the college.

True. The university has more students.

True. The university has less students.  

  False. The university has more students.

False. The university has less students.

(c) The sampling variability for the university is lower than that for the college.

True. The university has more students.

True. The university has less students.    

False. The university has more students.False.

The university has less students.

(d) No conclusion about the sampling variability can be stated without knowing the results of the study.

true

False. Because we know the approximate sample sizes, we can make some conclusions about the sampling variability ahead of time.    

False. We can always make a conclusion about the sampling variability.

none of the above

Explanation / Answer

It is known that

sample variability is inversely proportional to sample size.

Hence,

(a) The sampling variability is the same for both schools.

ans-> False. The sample sizes are different.

(b) The sampling variability for the university is higher than that for the college.

ans-> False. The university has more students.

(c) The sampling variability for the university is lower than that for the college.

ans-> True. The university has more students.

(d) No conclusion about the sampling variability can be stated without knowing the results of the study

ans-> False. Because we know the approximate sample sizes, we can make some conclusions about the sampling variability ahead of time.

since university sample size = 20,000 * 0.05 = 1000

college sample size = 5000 * 0.05 = 250

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