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Chapter 8: Q. R8.6 (page 548)

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 7 days. How large a sample would be required to obtain a margin of error of at most 0.01 in a 99% confidence interval for the population proportion who would say that they attended a religious service?

Short Answer

Expert verified

The required sample size is3152

Step by step solution

01

Given information

Confidence level=99%

Margin of error (E)=0.01

02

The objective is to find out the sample size to have a margin of error of at most 0.01at 99%a confidence level.

We know,

The formula to compute the sample size is:

n=p^(1-p^)z伪2E2

There is no information about p^provided here.

Hence, assume is to be 0.50.

According to the standard normal table, the value of za2corresponding to the 99%confidence level is2.576

The sample size can be calculated as:

localid="1654402152379" n=p^(1-p^)z伪2E2=0.50(1-0.50)(2.5760.01)2=3151.576鈮�3152

Therefore, the sample size is3152

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