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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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