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.
If the study were conducted repeatedly (selecting different samples of people each time), which one of the following would be true regarding the resulting sample proportions of "yes" responses?
a. Different sample proportions would result each time, but for sample size 100 they would be centered (have their mean) at the true population proportion, whereas for sample size 900 they would not.
b. For either sample size, using the same size each time, as long as the sampling is done with replacement, their mean would be 0.
c. Different sample proportions would result each time, but for sample size 900 they would be centered (have their mean) at the true population proportion, whereas for sample size 100 they would not.
d. Different sample proportions would result each time, but for either sample size, they would be centered (have their mean) at the true population proportion.