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.