Millionaires. Professor Thomas Stanley of Georgia State University has surveyed millionaires since 1973. Among other information, Professor Stanley obtains estimates for the mean age, μ, of all U.S. millionaires. Suppose that one year’s study involved a simple random sample of 36 U.S. millionaires whose mean age was 58.53 years with a sample standard deviation of 13.36 years.

a. If, for next year’s study, a confidence interval for μ is to have a margin of error of 2 years and a confidence level of 95%, determine the required sample size.

b. Why did you use the sample standard deviation,s = 13.36, in place of σ in your solution to part (a)? Why is it permissible to do so?