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 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.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.

Suppose we take repeated random samples of size 20 from a population with a mean of 60 and a standard deviation of 8. Which of the following statements is true about the sampling distribution of the sample mean (x̄)? Check all that apply. The distribution is normal regardless of the shape of the population distribution, because the sample size is large enough. The distribution will be normal as long as the population distribution is normal. The distribution's mean is the same as the population mean 60. The distribution's standard deviation is larger than the population standard deviation of 8.

For a large, top-rated corporation, 94% of employees said the corporation is a great place to work. Suppose that we will take a random sample of 7 employees. Let p̂ represent the proportion of employees from the sample who said the corporation is a great place to work. Consider the sampling distribution of the sample proportion p̂. Find the standard deviation (σ) of the sampling distribution of the sample proportion p̂. Round your answer to two decimal places.