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 ≈ 10.2 thousand dollars.
25.7 | 39.0 | 34.8 | 25.7 | 58.6 | 45.3 | 34.1 | 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 | 26.7 |
(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.
a) x =33.37
b)
sample size n= | 42.00 |
std deviation σ= | 10.20 |
std error ='σx=σ/√n= | 1.5739 |
for 75 % CI value of z= | 1.150 | |
margin of error E=z*std error = | 1.81 | |
lower bound=sample mean-E= | 31.56 | |
Upper bound=sample mean+E= | 35.18 |
Yes. This confidence interval suggests that the bank profits are less than those of other financial institutions.
d)
Yes. This confidence interval suggests that the bank profits are higher than those of other financial institutions.
e)
for 90 % CI value of z= | 1.645 | |
margin of error E=z*std error = | 2.59 | |
lower bound=sample mean-E= | 30.78 | |
Upper bound=sample mean+E= | 35.96 |
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 are higher than those of other financial institutions.
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