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.

1. Which of the following is true regarding the sample proportion p-hat, of "yes" responses?
   
   • The sample proportion from the sample of 900 is more likely to be close to the true population proportion, p.
   • The sample proportion from sample of 100 is more likely to be close to the true population proportion, p.
   • The sample proportion in either proposal is equally likely to be close to the true population proportion, p, since the sampling is random.
   • It is impossible to say one way or the other.
   
   
   
2. If the study were conducted over and over (selecting different samples of people each time), which one of the following would be true regarding the resulting sample proportions of "yes" responses?
   
   • 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.
   • 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.
   • Different sample proportions would result each time, but for either sample size, they would be centered (have their mean) at the true population proportion.
   • For either sample size, using the same size each time, as long as the sampling is done with replacement, their mean would be 0.
   • None of the above is true, since it makes no sense to talk about the mean of sample proportions.
   
   
   
3. Which one of the following is true regarding the standard deviation of the sampling distribution of the sample proportion, p-hat, of "yes" responses?
   
   • The standard deviation of the sampling distribution will be 9 times smaller with sample size 100.
   • The standard deviation of the sampling distribution will be 9 times larger with sample size 100.
   • The standard deviation of the sampling distribution will be 3 times smaller with sample size 100.
   • The standard deviation of the sampling distribution will be 3 times larger with sample size 100.
   • The standard deviation of the sampling distribution will be the same for both sample sizes.