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.

27.1	31.3	35.5	41.1	41.8	25.0	35.5	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	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) 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

Answer 1

The statistical software output for this problem is:

Hence,

a) x = 32.47

b) Lower limit = 31.24

Upper limit = 33.69

c) Lower limit = 30.70

Upper limit = 34.23