A political polling agency wants to take a random sample of registered voters and ask whether or not they will vote for a certain candidate. One plan is to select 400 voters, another plan is to select 1,600 voters.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? Different sample proportions would result each time, but for sample size 1,600 they would be centered (have their mean) at the true population proportion, whereas for sample size 400 they would not. For either sample size, using the same size each time, as long as the samples are drawn with replacement, they would be centered (have a mean) at 0. Different sample proportions would result each time, but for sample size 400 they would be centered (have their mean) at the true population proportion, whereas for sample size 1,600 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.

A political polling agency wants to take a random sample of registered voters and ask whether or not they will vote for a certain candidate. One plan is to select 400 voters, another plan is select 1,600 voters.Which of the following is true regarding the sample proportion p̂ of "yes" responses?Group of answer choicesThe sample proportion in either proposal is equally likely to be close to the true population proportion, p, since the sampling is random.The sample proportion from sample of 1,600 is more likely to be close to the true population proportion, p.The sample proportion from the sample of 400 is more likely to be close to the true population proportion, p.

A political polling agency wants to take a random sample of registered voters and ask whether or not they will vote for a certain candidate. One plan is to select 400 voters, another plan is to select 1,600 voters.Which one of the following is true regarding the standard deviation of the sampling distribution of the sample proportion, p̂, of "yes" responses? The standard deviation of the sampling distribution will be 4 times smaller with sample size 400. The standard deviation of the sampling distribution will be 4 times larger with sample size 400. The standard deviation of the sampling distribution will be 2 times smaller with sample size 400. The standard deviation of the sampling distribution will be 2 times larger with sample size 400. The standard deviation of the sampling distribution will be the same for both sample sizes.

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, p̂, of "yes" responses?Group of answer choicesThe standard deviation of the sampling distribution will be the same for both sample sizes.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 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.

A politician is interested in the proportion of voters in his district who think he is doing a good job. Define the following in terms of the study. Give examples where appropriate.Part (a)Part (b)The sampleThe sample is all the voters in the district who think the politician is doing a good job.The sample is all voters in the district.    The sample is a group of voters in the district who think the politician is doing a good job.The sample is a group of voters in the district.

Suppose that 20% of the residents in a certain state support an increase in the property tax. An opinion poll will randomly sample 400 state residents and will then compute the proportion in the sample that support a property tax increase.How likely is the resulting sample proportion to be within 0.04 of the true proportion (i.e., between 0.16 and 0.24)?(Hint: Use the sampling distribution of the sample proportion in this case.) It is certain that the resulting sample proportion will be within 0.04 of the true proportion. There is roughly a 99.7% chance that the resulting sample proportion will be within 0.04 of the true proportion. There is roughly a 95% chance that the resulting sample proportion will be within 0.04 of the true proportion. There is roughly a 68% chance that the resulting sample proportion will be within 0.04 of the true proportion.