Jobs and productivity! How do banks rate? One way to answer this question is to

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 ? ? 10.6 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.)

45.3 50.9 55.8 57.9 44.6 48.1 45.3 57.9 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

Explanation / Answer

The statistical software output for this problem is:

One sample Z confidence interval:
? : Mean of variable
Standard deviation = 10.6

75% confidence interval results:

Hence,

a) x = 35.82 thousand dollars

b) 75% confidence interval:

Lower limit = 33.94 thousand dollars

Upper limit = 37.70 thousand dollars

Variable n Sample Mean Std. Err. L. Limit U. Limit Data 42 35.816667 1.6356155 33.935137 37.698196

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