Need Help Solving A Stat Question

Question

What sample size is needed to give a margin of error within  in estimating a population mean with 99% confidence, assuming a previous sample had s = 3.9

Answer 1

We know that the formula to find a confidence interval is:

Confidence Interval = x̄ ± z* (s / √n)

In this formula, the part on the right of the ± sign gives you your margin of error. Next, to find our critical value, z*, you can type the following into your calculator:

invNorm(0.99, 0, 1)

This function finds the z-score value corresponding to the 99th percentile. The answer to this should be 2.326. We also know the standard deviation is 3.9 as mentioned in the problem.

Plugging this information into the margin of error formula, you should have this equation:

margin of error = 2.326 * (3.9 / √n)

With some algebra, you can rearrange your formula to solve for n:

n = [3.9 / (margin of error/2.326)]²

Whatever value was written in the question between the words "within" and "in" would be your margin of error, which you would plug into the above formula to solve for n.