Wk 7 Question 4

A social scientist wishes to conduct a survey. She plans to ask a yes/no question to a random sample from the U.S. adult population. One proposal is to select 100 people; another proposal is to select 900 people. Which one of the following is true regarding the standard deviation of the sampling distribution of the sample proportion, p-hat, of "yes" responses?

A The standard deviation of the sampling distribution will be 9 times smaller with sample size 100.

B The standard deviation of the sampling distribution will be 9 times larger with sample size 100.

C The standard deviation of the sampling distribution will be 3 times smaller with sample size 100.

D The standard deviation of the sampling distribution will be 3 times larger with sample size 100.

E The standard deviation of the sampling distribution will be the same for both sample sizes.