Jobs and productivity! How do banks rate? One way to answer this question is to examine annual profits per employee. The following is data about annual profits per employee (in units of1 thousanddollars per employee) for representative companies in financial services. Assume9.4thousanddollars.

37.6 39.7 25.0 43.9 27.8 29.2 52.3 58.6 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) Use a calculator or appropriate computer software to findxfor the preceding data. (Round your answer to two decimal places.)

• ________thousand dollars

(b) Let us say that the preceding data are representative of the entire sector of (successful) financial services corporations. Find a75% confidenceinterval for, the average annual profit per employee for all successful banks. (Round your answers to two decimal places.)

• lower limit_________thousand dollars
• upper limit_________thousand dollars

(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 than30 thousanddollars per employee. Do you think this might be somewhat low compared with other successful financial institutions? Explain by referring to the confidence interval you computed inpart (b). (choose one)

• 1. Yes. This confidence interval suggests that the bank profits are less than those of other financial institutions.
• 2. Yes. This confidence interval suggests that the bank profits do not differ from those of other financial institutions.
• 3. No. This confidence interval suggests that the bank profits are less than those of other financial institutions.
• 4. No. This confidence interval suggests that the bank profits do not differ from those of other financial institutions.

(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 inpart (b).

• 1. No. This confidence interval suggests that the bank profits are higher than those of other financial institutions.
• 2. No. This confidence interval suggests that the bank profits do not differ from those of other financial institutions.
• 3. Yes. This confidence interval suggests that the bank profits are higher than those of other financial institutions.
• 4. Yes. This confidence interval suggests that the bank profits do not differ from those of other financial institutions.

(e) Find a 90% confidence interval for, the average annual profit per employee for all successful banks. (Round your answers to two decimal places.)

• lower limit_______thousand dollars
• upper limit_______thousand dollars

(f) 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 than30 thousanddollars per employee. Do you think this might be somewhat low compared with other successful financial institutions? Explain by referring to the confidence interval you computed inpart (e).

• 1. Yes. This confidence interval suggests that the bank profits are less than those of other financial institutions.
• 2. Yes. This confidence interval suggests that the bank profits do not differ from those of other financial institutions.
• 3. No. This confidence interval suggests that the bank profits are less than those of other financial institutions.
• 4. No. This confidence interval suggests that the bank profits do not differ from those of other financial institutions.

(g) 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 inpart (e).

• 1. No. This confidence interval suggests that the bank profits are higher than those of other financial institutions.
• 2. No. This confidence interval suggests that the bank profits do not differ from those of other financial institutions.
• 3. Yes. This confidence interval suggests that the bank profits are higher than those of other financial institutions.
• 4. Yes. This confidence interval suggests that the bank profits do not differ from those of other financial institutions.