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Chapter 8: Q.6 (page 523)

Do you go to church? The Gallup Poll plans to ask a random sample of adults whether they attended a religious service in the last 7days. How large a sample would be required to obtain a margin of error of 0.01ina99%confidence interval for the population proportion who would say that they attended a religious service? Show your work.

- Construct and interpret a confidence interval for a population proportion.

- Explain how practical issues like nonresponse, under coverage, and response bias can affect the interpretation of a confidence interval.

Short Answer

Expert verified

The sample size is 1657716577

Step by step solution

01

Step-1 Given Information

Given in the question that,

Margin of errorE=1%=0.01

Confidence level=99%we have to find How large a sample would be required to obtain a margin of error and confidence interval for the population proportion who would say that they attended a religious service.

02

Step-2 Explanation

The formula to compute the sample size is:

n=p铃�1-p^zE2

Calculation:

From the standard normal table, the z-score at 99%confidence level is 2.576.

Consider, sample proportion to be 0.05.

The sample size is calculated as:

n=p^1-p^zE2

=0.501-0.502.5760.012=0.501-0.502.5760.012

=16577

Thus, the sample size is 16577.

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Most popular questions from this chapter

High tuition costs Glenn wonders what proportion of the students at his school think that tuition is too high. He interviews an SRS of 50 of the 2400 students at his college. Thirty-eight of those interviewed think tuition is too high.

True or false: The interval from 2.84to 7.55has a 95%chance of containing the actual population standard deviation S. Justify your answer.

Refer to Exercise 12. As Gallup indicates, the 3percentage point margin of error for this poll includes only sampling variability (what they call 鈥渟ampling error鈥�). What other potential sources of error (Gallup calls these 鈥渘on-sampling errors鈥�) could affect the accuracy of the59% estimate?

The body mass index (BMI) of all American young women is believed to follow a Normal distribution with a standard deviation of about 7.5. How large a sample would be needed to estimate the mean BMI M in this population to within 卤1vwith 99% confidence? Show your work.

In each of the following situations, discuss whether it would be appropriate to construct a one-sample tinterval to estimate the population mean.

(a) We want to estimate the average age at which U.S. presidents have died. So we obtain a list of all U.S. presidents who have died and their ages at death.

(b) How much time do students spend on the Internet? We collect data from the 32members of our AP Statistics class and calculate the mean amount of time that each student spent on the Internet yesterday.

(c) Judy is interested in the reading level of a medical journal. She records the length of a random sample of 100words from a multipage article. The Minitab histogram below displays the data.
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