Jobs and productivity! How do banks rate? One way to answer this question is to
ID: 3174110 • Letter: J
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 one thousand dollars per employee) for representative companies in financial services. Assume 9.6 thousand dollars.
(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 , the average annual profit per employee for all successful banks. (Round your answers to two decimal places.)
lower limit
upper limit
(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 , the average annual profit per employee for all successful banks. (Round your answers to two decimal places.)
lower limit
upper limit
(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.
42.5 28.5 57.9 45.3 34.8 42.5 36.2 39.7 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 26.7Explanation / Answer
(a) n=42, sum=1425.9,
sample mean x =sum/n=1425.9/42=33.95
(b) here standard deviation(sd)=sigma=9.6, n=42
(1-alpha)*100% confidence interval for mean=mean± z(alpha/2)*sd/sqrt(n)
75% confidence interval for mean=mean±z(0.25/2)*sd/sqrt(n)=33.95±1.15*9.6/sqrt(42)=33.95±1.70=(32.25,35.65)
lower 32.25 thousand and upper 35.65 thousand
(c) Yes. This confidence interval suggests that the bank profits are less than those of other financial institutions.
since 30000 is less than the lower limit of confidence interval 32.25 thousand
(d) Yes. This confidence interval suggests that the bank profits are higher than those of other financial institutions.
yes, 40000 is more than upper limit of the confidence interval 35.65
(e)
here standard deviation(sd)=sigma=9.6, n=42
(1-alpha)*100% confidence interval for mean=mean± z(alpha/2)*sd/sqrt(n)
90% confidence interval for mean=mean±z(0.25/2)*sd/sqrt(n)=33.95±1.645*9.6/sqrt(42)=33.95±2.44=(31.51,36.39)
lower 31.51 thousand and upper 36.39 thousand
(f) Yes. This confidence interval suggests that the bank profits are less than those of other financial institutions.
since 30000 is less than the lower limit of confidence interval 31.51 thousand
(g)Yes. This confidence interval suggests that the bank profits are higher than those of other financial institutions.
yes, 40000 is more than upper limit of the confidence interval 36.39
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