A personality test has a subsection designed to assess the “honesty” of the test-taker. Suppose that you’re interested in the meanscore on this subsection among the general population. You decide that you’ll use the mean of a random sampleof scores on this subsection to estimate the population mean. What is the minimum sample size needed in order for you to be 99% confident that your estimate is within4 of the population mean. Use the value 23 for the population standard deviationof scores on this subsection.

Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).

This problem shows how to find the sample size necessary to estimate a population mean with a sample mean. The confidence level, a bound on the margin of error, and an estimate of the population standard deviation are given. Using this information, we find the necessary sample size.