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 ≈ 10.8 thousand dollars. 59.3 32.7 54.4 58.6 59.3 27.1 28.5 43.9 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
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 ≈ 10.8 thousand dollars.
| 59.3 | 32.7 | 54.4 | 58.6 | 59.3 | 27.1 | 28.5 | 43.9 | 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 |
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 |
Solution:
It is given:
(a) Use a calculator or appropriate computer software to find x for the preceding data. (Round your answer to two decimal places.)
Answer: The steps to be followed in TI-84 are:
Press STAT and then click on Edit
Enter the given data under L1
Press STAT and scroll right to CALC
Scroll to 1- Vars Stat L1
Press Enter and the output will contain the sample mean.
(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.)
Answer: The 75% confidence interval is:
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