Question

Jobs and productivity! How do retail stores rate? One way to answer this question is to examine annual profits per employee. The following data give annual profits per employee (in units of one thousand dollars per employee) for companies in retail sales. Assume σ ≈ 3.6 thousand dollars.

4.4	6.0	4.5	8.4	8.5	5.0	9.0	6.5	2.6	2.9	8.1	−1.9
11.9	8.2	6.4	4.7	5.5	4.8	3.0	4.3	−6.0	1.5	2.9	4.8
−1.7	9.4	5.5	5.8	4.7	6.2	15.0	4.1	3.7	5.1	4.2

(a) Use a calculator or appropriate computer software to find x for the preceding data. (Round your answer to two decimal places.)
thousand dollars per employee

(b) Let us say that the preceding data are representative of the entire sector of retail sales companies. Find an 80% confidence interval for μ, the average annual profit per employee for retail sales. (Round your answers to two decimal places.)

lower limit	thousand dollars
upper limit	thousand dollars

(e) Find an 95% confidence interval for μ, the average annual profit per employee for retail sales. (Round your answers to two decimal places.)

lower limit	thousand dollars
upper limit	thousand dollars

Answer 1

a)
xbar = 5.09

b)
sample mean, xbar = 5.09
standard deviation, sigma = 3.6
sample size, n = 35

For 80% Confidence level, the z-value = 1.28

CI = (xbar - z*sigma/sqrt(n), xbar + z*sigma/sqrt(n))
CI = (5.09 - 1.28 * 3.6/sqrt(35) , 5.09 + 1.28 * 3.6/sqrt(35))
CI = (4.31 , 5.87)

lower limit = 4.31 thousand dollars
upper limit = 5.87 thousand dollars

e)
For 95% Confidence level, the z-value = 1.96

CI = (xbar - z*sigma/sqrt(n), xbar + z*sigma/sqrt(n))
CI = (5.09 - 1.96 * 3.6/sqrt(35) , 5.09 + 1.96 * 3.6/sqrt(35))
CI = (3.9 , 6.28)

lower limit = 3.90 thousand dollars
upper limit = 6.28 thousand dollars