The next three questions refer to the following information:

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 8100 people.

Question 2 of 6

Question 2

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Which of the following is true regarding the sample proportion p-hat, of "yes" responses?

The sample proportion from the sample of 8100 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.

Question 3 of 6

Question 3

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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?

None of the above is true, since it makes no sense to talk about the mean of sample proportions.

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 8100 they would not.

Different sample proportions would result each time, but for sample size 8100 they would be centered (have their mean) at the true population proportion, whereas for sample size 100 they would not.

For either sample size, using the same size each time, as long as the sampling is done with replacement, their mean would be 0.

Different sample proportions would result each time, but for either sample size, they would be centered (have their mean) at the true population proportion.

Question 4 of 6

Question 4

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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 larger with sample size 100.

The standard deviation of the sampling distribution will be 81 times smaller with sample size 100.

The standard deviation of the sampling distribution will be 81 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 the same for both sample sizes.

Question 5 of 6

Question 5

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The sampling distribution of a statistic is (select the best answer):

The mechanism that determines whether the random sampling was effective.

A normal curve, for which probabilities are obtained by standardizing.

A distribution of all parameters from the population that is to be randomly sampled.

A distribution of all possible summary statistics from a single random sample, from the same population.

None of the above

Question 6 of 6

Question 6

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Suppose that 20% of the residents in a certain state support an increase in the property tax. An opinion poll will randomly sample 900 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 .02 of the true proportion (i.e., between .18 and .22)?

(Hint: Use the sampling distribution of the sample proportion in this case.)

There is roughly a 95% chance that the resulting sample proportion will be within .02 of the true proportion.

It is certain that the resulting sample proportion will be within .02 of the true proportion.

There is roughly a 99.7% chance that the resulting sample proportion will be within .02 of the true proportion.

There is roughly a 68% chance that the resulting sample proportion will be within .02 of the true proportion.