Question

5 4-19 points BBUnderStat12 7.1.024. G My Notes Ask Your Teacher 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 1 thousand dollars per employee) for companies in retail sales. Assume a 4.0 thousand dollars 4.1 6.4 4.0 9.0 7.9 5.8 8.8 5.7 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 4.11 3.7 5.11 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 , the average annual profit per employee for retail sales. (Round your answers to two decimal places.) lower limit thousand dollars upper limit thousand dollars (C) Let us say that you are the manager of a retail store with a large number of employees. Suppose the annual profits are less than 3 thousand dollars per employee. Do you think this might be low compared with other retail stores? Explain by referring to the confidence interval you computed in part (b). OYes. This confidence interval sugaests that the profits per employee are less thn those of other retail stores ONo. This confidence interval suggests that the profits per employee do not differ from those of other retal stores. (d) Suppose the annual profits are more than 6.5 thousand dollars per employee. As store manager, would you feel somewhat better? Explain by referring to the confidence interval you computed in part (b). Yes. This confidence interval suggests that the profits per employee are greater than those of other retail stores. No. This confidence Interval suggests that the profits per employee do not differ from those of other retail stores (e) Find an 95% confidence interval for . the average annual profit per employee for retal sales. (Round your answers too two decimal places.) lower limit thousand dollars upper imit thousand dolars 27 P V40de ING O Type here to search 1/a/2019

Answer 1

We have,

sample size: n = 35

Population standard deviation:

o =4

a) Mean of data set: (using Excel average function)

thousand dollars per employee

T = 5.068571429 5.07

b) 80% confidence interval

Confidence level: c = 0.8

Level of significance:

a=1-0.8 = 0.2

L'O=

Find corresponding z score:

29 = 20.1 = 1.28

Confidence interval formula:

CI = 7 土々*

Plugging in all values we get,

CI = 5.07 – 1.28 * 32

$\Rightarrow CI=5.07\pm0.8654$

→ CI = (4.2046,5.9354) (4.20,5.94)

Lower limit: 4.20 thousand dollars

Upper limit: 5.94 thousand dollars

c) At 80% of confidence level average profit per employee lies within 4.20 thousand dollars to 5.94 thousand dollars. 3 thousand dollars is far less than the lower limit of confidence interval.

Hence this confidence interval suggest that the profits per employee are less than those of other retail stores.

Yes. This confidence interval suggest that the profits per employee are less than those of other retail stores.

d) At 80% of confidence level average profit per employee lies within 4.20 thousand dollars to 5.94 thousand dollars. 6.5 thousand dollars is far above than the upper limit of confidence interval.

Hence this confidence interval suggest that the profits per employee are greater than those of other retail stores.

Hence yes as a store manager I will feel better.

Yes. This confidence interval suggest that the profits per employee are greater than those of other retail stores.

e) 95% confidence interval

Confidence level: c = 0.95

Level of significance:

a=1-0.95 = 0.05

= = 0.025

Find corresponding z score:

29 = 20.025 = 1.96

Confidence interval formula:

CI = 7 土々*

Plugging in all values we get,

CI = 5.07 1.96 *

CI = 5.07 +1.3252

CI = (3.7448, 6.3952) (3.74, 6.4)

Lower limit: 3.74 thousand dollars

Upper limit: 6.4 thousand dollars