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Chapter 7: Q. T7.2 (page 486)

The Gallup Poll has decided to increase the size of its random sample of voters from about 1500 people to about 4000 people right before an election. The poll is designed to estimate the proportion of voters who favor a new law banning smoking in public buildings. The effect of this increase is to

a. reduce the bias of the estimate.

b. increase the bias of the estimate.

c. reduce the variability of the estimate.

d. increase the variability of the estimate.

e. reduce the bias and variability of the estimate.

Short Answer

Expert verified

(c) The effect of this increase is to reduce the variability of the estimate.

Step by step solution

01

Given Information

Right before an election, the Gallup Poll decided to raise the size of its random sample of voters from 1500 to 4000 persons. The purpose of the poll is to determine the percentage of voters who support a new law prohibiting smoking in public places.

02

Explanation for correct option

Because the inaccuracies are produced by the sampling techniques, sample size has no bearing on them. When the sample size is increased, the variability is reduced since a larger sample provides more information about the population and thus better estimates.

As a result, the best solution is (c)

03

Explanation for incorrect option

a. reduce the bias of the estimate is not the answer.

b. increase the bias of the estimate is not the answer.

d. increase the variability of the estimate is not the answer.

e. reduce the bias and variability of the estimate is not the answer.

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Most popular questions from this chapter

Suppose that the sample proportion of students who did all their assigned homework last week is p^=57100=0.57. Would this sample proportion provide convincing evidence that less than 60%of all students at the school completed all their assigned homework last week? Explain your reasoning.

The number of undergraduates at Johns Hopkins University is approximately 2000 , while the number at Ohio State University is approximately 60,000. At both schools, a simple random sample of about 3%of the undergraduates is taken. Each sample is used to estimate the proportion p of all students at that university who own an iPod. Suppose that, in fact, p=0.80 at both schools. Which of the following is the best conclusion?

a. We expect that the estimate from Johns Hopkins will be closer to the truth than the estimate from Ohio State because it comes from a smaller population.

b. We expect that the estimate from Johns Hopkins will be closer to the truth than the estimate from Ohio State because it is based on a smaller sample size.

c. We expect that the estimate from Ohio State will be closer to the truth than the estimate from Johns Hopkins because it comes from a larger population.

d. We expect that the estimate from Ohio State will be closer to the truth than the estimate from Johns Hopkins because it is based on a larger sample size.

e. We expect that the estimate from Johns Hopkins will be about the same distance from the truth as the estimate from Ohio State because both samples are 3 % of their populations.

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a. Find the probability that the sample mean area is 249.6ft2or less if the manufacturer鈥檚 claim is true.

b. Based on your answer to part (a), is there convincing evidence that the company is overstating the average area of its aluminum foil rolls?

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