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Question

The $2003 ~Statistical ~Abstract ~of ~the ~United ~States$ reported the percentage of people $18$ years of age and older who smoke. Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of $.30.$

How large a sample should be taken to estimate the proportion of smokers in the population with a margin of error of $.02$? Use $95\%$ confidence.

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

Step 1

1 of 6Given:

- $p^*$ = Preliminary estimate = 30% = 0.30
- $c$ = Confidence level = 95% = 0.95
- $E$ = Margin of error = 0.02

In this exercise, we determine the required minimum sample size.

*How can the formula of the sample size be derived from the confidence interval?*

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