Jobs and productivity! How do banks rate? One way to answer this question is to examine annual profits per employee. Forbes Top Companies, edited by J. T. Davis (John Wiley & Sons), gave the following data about annual profits per employee (in units of one thousand dollars per employee) for representative companies in financial services. Companies such as Wells Fargo, First Bank System, Key Banks, Norwest Banks, and so on were included.

42.9 43.8 48.2 60.6 54.9 55.1 52.9 54.9 42.5 33.0 33.6 36.9 27.0 47.1 33.8 28.1 28.5 29.1 36.5 36.1 26.9 27.8 28.8 29.3 31.5 31.7 31.1 38.0 32.0 31.7 32.9 23.1 54.9 43.8 36.9 31.9 25.5 23.2 29.8 22.3 26.5 26.7

(a) Verify that for the preceding data ¯x = 36.0 and s = 10.2 approximately.

(b) Let us say that the preceding data are representative of the entire sector of (successful) financial services corporations. Find a 75% confidence interval for µ, the average annual profit per employee for all successful banks.

(c) Let us say that you are the manager of a local bank with a large number of employees. Suppose the annual profits per employee are less than 30 thousand dollars per employee. Do you think that this might be somewhat low compared with other successful financial institutions? Explain by referring to the confidence interval you computed in (b).

(d) Suppose the annual profits are more than 40 thousand dollars per employee. As manager of the bank, would you feel somewhat better? Explain by referring to the confidence interval you computed in (b).

(e) Repeat (b), (c), and (d) for a 90% confidence level.