Question
In: Statistics and Probability
Jobs and productivity! How do banks rate? One way to answer this question is to examine...
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 ≈ 9.4 thousand dollars.
53.0 34.8 60.0 46.7 33.4 26.4 57.9 48.1 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
1. Use a calculator or appropriate computer software to find x
for the preceding data. (Round your answer to two decimal
places.)
_____ thousand dollars
2. 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.)
(a) lower limit = thousand dollars
(b) upper limit = thousand dollars
3. 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 (2).
(a) Yes. This confidence interval suggests that the bank
profits are less than those of other financial institutions.
(b) Yes. This confidence interval suggests that the bank
profits do not differ from those of other financial
institutions.
(c) No. This confidence interval suggests that the bank
profits are less than those of other financial institutions.
(d) No. This confidence interval suggests that the bank
profits do not differ from those of other financial
institutions.
4. 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 (2).
(a) No. This confidence interval suggests that the bank
profits are higher than those of other financial
institutions.
(b) No. This confidence interval suggests that the bank
profits do not differ from those of other financial
institutions.
(c) Yes. This confidence interval suggests that the bank
profits are higher than those of other financial
institutions.
(d) Yes. This confidence interval suggests that the bank
profits do not differ from those of other financial
institutions.
5. Find a 90% confidence interval for μ, the average annual
profit per employee for all successful banks. (Round your answers
to two decimal places.)
(a) lower limit = thousand dollars
(b) upper limit = thousand dollars
(6. 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 (5).
(a) Yes. This confidence interval suggests that the bank
profits are less than those of other financial institutions.
(b) Yes. This confidence interval suggests that the bank
profits do not differ from those of other financial
institutions.
(c) No. This confidence interval suggests that the bank
profits are less than those of other financial institutions.
(d) No. This confidence interval suggests that the bank
profits do not differ from those of other financial
institutions.
7. 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 5.
(a) No. This confidence interval suggests that the bank
profits are higher than those of other financial
institutions.
(b) No. This confidence interval suggests that the bank
profits do not differ from those of other financial
institutions.
(c) Yes. This confidence interval suggests that the bank
profits are higher than those of other financial
institutions.
(d) Yes. This confidence interval suggests that the bank
profits do not differ from those of other financial
institutions.
Solutions
Expert Solution
using excel>addin>phstat>confidence interval
we have
| Confidence Interval Estimate for the Mean | |
| Data | |
| Population Standard Deviation | 9.4 |
| Sample Mean | 34.73333333 |
| Sample Size | 42 |
| Confidence Level | 75% |
| Intermediate Calculations | |
| Standard Error of the Mean | 1.4505 |
| Z Value | -1.1503 |
| Interval Half Width | 1.6685 |
| Confidence Interval | |
| Interval Lower Limit | 33.06 |
| Interval Upper Limit | 36.40 |
1. sample mean for the preceding data.
34.73 thousand dollars
2. 75% confidence interval for μ
(a) lower limit = 33.06 thousand dollars
(b) upper limit = 36.40 thousand dollars
3.
(c) No. This confidence interval suggests that the bank profits are less than those of other financial institutions.
4. 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 (2).
(a) No. This confidence interval suggests that the bank profits are higher than those of other financial institutions.
| Confidence Interval Estimate for the Mean | |
| Data | |
| Population Standard Deviation | 9.4 |
| Sample Mean | 34.73333333 |
| Sample Size | 42 |
| Confidence Level | 90% |
| Intermediate Calculations | |
| Standard Error of the Mean | 1.4505 |
| Z Value | -1.6449 |
| Interval Half Width | 2.3858 |
| Confidence Interval | |
| Interval Lower Limit | 32.35 |
| Interval Upper Limit | 37.12 |
5. Find a 90% confidence interval for μ, the average annual profit per employee for all successful banks. (Round your answers to two decimal places.)
(a) lower limit = 32.35 thousand dollars
(b) upper limit = 37.12 thousand dollars
(6. 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 (5).
(c) No. This confidence interval suggests that the bank profits are less than those of other financial institutions.
7. 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 5.
(a) No. This confidence interval suggests that the bank profits are higher than those of other financial institutions.
orchestra answered 1 year agoRelated Solutions
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50.2
48.1
53.0
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Jobs and productivity! How do banks rate? One way to answer this question is to examine...
Jobs and productivity! How do banks rate? One way to answer this
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Jobs and productivity! How do banks rate? One way to answer this question is to examine...
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
thousanddollars per employee) for representative companies in
financial services. Assume σ ≈ 10.0 thousand dollars.
46.7
29.2
43.2
53.7
50.2
46.7
53.0
49.5
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...
Jobs and productivity! How do banks rate? One way to answer this question is to examine...
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 ≈ 10.7 thousand dollars.
43.2
46.0
56.5
46.0
31.3
58.6
57.2
60.0
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...
Jobs and productivity! How do banks rate? One way to answer this question is to examine...
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
thousanddollars per employee) for representative companies in
financial services. Assume σ ≈ 9.1 thousand dollars.
41.8
45.3
43.2
53.7
26.4
48.8
48.1
32.7
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...
Jobs and productivity! How do banks rate? One way to answer this question is to examine...
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 ≈ 9.4 thousand dollars.
43.9
36.2
27.8
58.6
25.0
36.2
39.7
60.0
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...
Jobs and productivity! How do banks rate? One way to answer this question is to examine...
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 ≈ 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...
Jobs and productivity! How do banks rate? One way to answer this question is to examine...
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 ≈ 9.1 thousand dollars.
46.7
45.3
32.7
38.3
39.7
46.7
46.0
40.4
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...
1.) Jobs and productivity! How do banks rate? One way to answer this question is to...
1.) 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 ≈ 9.8 thousand dollars.
46.7
41.8
53.7
34.8
27.8
34.8
25.7
56.5
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...
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