Confidence interval for the population mean.
Jobs and productivity! How do retail stores rate? One way to answer this problem 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. Companies such as Gap, Nordstrom, Circuit City, Dillards, JCPenny, Sears, WalMart, Office Depot and Toys 'R' Us are included. presume σ = 3.8 thousand dollars.
4.4

6.5

4.2

8.9

8.7

8.1

6.1

6.0

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) Utilize a calculator or appropriate computer software to verify that, for the preceding data, xbar = 5.1.
(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.
(c) Let us say you are a manager of a retail store with a large number of employees. Suppose annual profits per employee are less than 3 thousand dollars per employee. Do you think that this might be low compared with other retail stores/ describe by referring to the confidence interval you computed in part (b)?
(d) Presume the annual profits are more than 6.5 thousand dollars per employee. As store manager, would you feel somewhat better? Give details by referring to the confidence interval you computed in part (b).
(e) Repeat parts (b0, (c), and (d) for a 95% confidence interval.