Question

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 of 1 thousand dollars per employee) for representative companies in financial services. Assume σ ≈ 11.0 thousand dollars. 57.9 31.3 56.5 27.1 35.5 27.8 39.0 53.0 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 find x for 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 a 75% confidence interval for μ, 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 than 30 thousand dollars 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 in part (b). Yes. This confidence interval suggests that the bank profits are less than those of other financial institutions. Yes. This confidence interval suggests that the bank profits do not differ from those of other financial institutions. No. This confidence interval suggests that the bank profits are less than those of other financial institutions. 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 in part (b). No. This confidence interval suggests that the bank profits are higher than those of other financial institutions. No. This confidence interval suggests that the bank profits do not differ from those of other financial institutions. Yes. This confidence interval suggests that the bank profits are higher than those of other financial institutions. 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 μ, 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 than 30 thousand dollars 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 in part (e). Yes. This confidence interval suggests that the bank profits are less than those of other financial institutions. Yes. This confidence interval suggests that the bank profits do not differ from those of other financial institutions. No. This confidence interval suggests that the bank profits are less than those of other financial institutions. 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 in part (e). No. This confidence interval suggests that the bank profits are higher than those of other financial institutions. No. This confidence interval suggests that the bank profits do not differ from those of other financial institutions. Yes. This confidence interval suggests that the bank profits are higher than those of other financial institutions. Yes. This confidence interval suggests that the bank profits do not differ from those of other financial institutions.

Answer 1

using excel>addin>phstat>confidence interval

we have

Confidence Interval Estimate for the Mean
Data
Population Standard Deviation	11
Sample Mean	33.96666667
Sample Size	42
Confidence Level	75%
Intermediate Calculations
Standard Error of the Mean	1.6973
Z Value	-1.1503
Interval Half Width	1.9525
Confidence Interval
Interval Lower Limit	32.01
Interval Upper Limit	35.92

(a) the sample mea is 33.97

(b) a 75% confidence interval for μ, the average annual profit per employee for all successful banks.

lower limit = 32.01 thousand dollars

upper limit = 35.92 thousand dollars

(c) . No. This confidence interval suggests that the bank profits do not differ from those of other financial institutions.

(d) No. This confidence interval suggests that the bank profits do not differ from those of other financial institutions]

Confidence Interval Estimate for the Mean
Data
Population Standard Deviation	11
Sample Mean	33.96666667
Sample Size	42
Confidence Level	90%
Intermediate Calculations
Standard Error of the Mean	1.6973
Z Value	-1.6449
Interval Half Width	2.7919
Confidence Interval
Interval Lower Limit	31.17
Interval Upper Limit	36.76

(e) a 90% confidence interval for μ, the average annual profit per employee for all successful banks. (

lower limit = 31.17 thousand dollars

upper limit = 36.76 thousand dollars

(f) . No. This confidence interval suggests that the bank profits do not differ from those of other financial institutions.

(g) No. This confidence interval suggests that the bank profits do not differ from those of other financial institutions.