The Statistical Abstract of the United States reported the percentage of people age 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 0.12. How large a sample should be taken to estimate the actual proportion of smokers with a margin of error of 0.02

A sample of 1015 should be taken.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

The margin of error is of:

Suppose that a study designed to collect new data on smokers and nonsmokers uses a preliminary estimate of the proportion who smoke of 0.12.

This means that

95% confidence level

So , z is the value of Z that has a pvalue of , so . I used 95% because the confidence level was not given.

How large a sample should be taken to estimate the actual proportion of smokers with a margin of error of 0.02?

This is n for which M = 0.02. So

Rounding up:

A sample of 1015 should be taken.