Jobs and productivity! How do banks rate? One way to answer thisquestion is to examine annual profits per employee. The followingis data about annual profits per employee (in units of 1 thousanddollars per employee) for representative companies in financialservices. Assume σ ≈ 9.3 thousand dollars.
| 54.4 | 35.5 | 53.7 | 59.3 | 41.8 | 26.4 | 52.3 | 27.8 | 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 findx for the preceding data. (Round your answer to twodecimal places.)
thousand dollars
(b) Let us say that the preceding data are representative of theentire sector of (successful) financial services corporations. Finda 75% confidence interval for μ, the average annual profitper employee for all successful banks. (Round your answers to twodecimal places.)
| lower limit    | thousand dollars |
| upper limit    | thousand dollars |
(c) Let us say that you are the manager of a local bank with alarge number of employees. Suppose the annual profits per employeeare less than 30 thousand dollars per employee. Do you think thismight be somewhat low compared with other successful financialinstitutions? Explain by referring to the confidence interval youcomputed in part (b).
Yes. This confidence interval suggests that the bank profits areless than those of other financial institutions.Yes. Thisconfidence interval suggests that the bank profits do not differfrom those of other financialinstitutions.     No. This confidenceinterval suggests that the bank profits are less than those ofother financial institutions.No. This confidence interval suggeststhat the bank profits do not differ from those of other financialinstitutions.
(d) Suppose the annual profits are more than 40 thousand dollarsper employee. As manager of the bank, would you feel somewhatbetter? Explain by referring to the confidence interval youcomputed in part (b).
No. This confidence interval suggests that the bank profits arehigher than those of other financial institutions.No. Thisconfidence interval suggests that the bank profits do not differfrom those of other financialinstitutions.     Yes. This confidenceinterval suggests that the bank profits are higher than those ofother financial institutions.Yes. This confidence interval suggeststhat the bank profits do not differ from those of other financialinstitutions.
(e) Find a 90% confidence interval for μ, the averageannual profit per employee for all successful banks. (Round youranswers 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 alarge number of employees. Suppose the annual profits per employeeare less than 30 thousand dollars per employee. Do you think thismight be somewhat low compared with other successful financialinstitutions? Explain by referring to the confidence interval youcomputed in part (e).
Yes. This confidence interval suggests that the bank profits areless than those of other financial institutions.Yes. Thisconfidence interval suggests that the bank profits do not differfrom those of other financialinstitutions.     No. This confidenceinterval suggests that the bank profits are less than those ofother financial institutions.No. This confidence interval suggeststhat the bank profits do not differ from those of other financialinstitutions.
(g) Suppose the annual profits are more than 40 thousand dollarsper employee. As manager of the bank, would you feel somewhatbetter? Explain by referring to the confidence interval youcomputed in part (e).
No. This confidence interval suggests that the bank profits arehigher than those of other financial institutions.No. Thisconfidence interval suggests that the bank profits do not differfrom those of other financialinstitutions.     Yes. This confidenceinterval suggests that the bank profits are higher than those ofother financial institutions.Yes. This confidence interval suggeststhat the bank profits do not differ from those of other financialinstitutions.
