Estimating a Population Mean when we don't know σ: Example 02

EXAMPLE Constructing a Confidence Interval
Listed in the stemplot are the ages of applicants who were unsuccessful in winning promotion*. There is an important larger issue of whether these applicants suffered age discrimination, but for now we will focus on the simple issue of using those values as a sample for the purpose of estimating the mean of a larger population.
Assume that the sample is a simple random sample and use the sample data with a 95% confidence level to find both of the following:
a. The margin of error E.
b. The confidence interval for 𝜇
*based on data from “Debating the Use of Statistical Evidence in Allegations of Age Discrimination,” by Barry and Boland, American Statistician, Vol. 58, No. 2.