A researcher would like to estimate the population proportion of adults living in a certain town who have at least a high school education. No more information is available about its value. How large of a sample size is needed to estimate it to within 0.15 of the true value with 99% confidence?

We would need a sample of size at least 74.

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:

99% confidence level

So , z is the value of Z that has a pvalue of , so .

How large of a sample size is needed to estimate it to within 0.15 of the true value with 99% confidence?

We need a sample of size at least n

n is found when

We don't know the proportion, so we estimate , which is the case for which we are going to need the largest sample size.

Rounding up

We would need a sample of size at least 74.