Chapter 7, Problem 7.17P

$\boxed{PA}$ The city manager has received a complaint from the local union of firefighters to the effect that they are underpaid. Not having much time, the city manager gathers the records of a random sample of 27 firefighters and finds that their average salary is $\$38,073$, with a standard deviation of $\$575$. If she knows that the average salary nationally is $\$38,202$, how can she respond to the complaint? Should she use a one-tailed test in this situation? Why? What would she say in a memo to the union that would respond to the complaint?