A company studied two programs for compensating its sales st

A company studied two programs for compensating its sales staff. In program A, salespeople were paid a higher salary, plus a small commission for each item they sold. In program B, they were paid a lower salary with a larger commission. Following are the amounts sold, in thousands of dollars, for each salesperson on each program.

Salesperson

Program

1

2

3

4

5

6

7

8

9

A

55

22

34

22

25

61

55

36

68

B

53

24

36

28

31

61

58

38

72

The same random sample of nine salespeople were observed under program A and B both. Since the sample size is so small (only 9), people may not want to assume any particular shape for the population distribution. (Please use Minitab software )to do a BOOTSTRAP procedure (with 1000 bootstrap samples) to answer the following questions.

a) Draw a histogram of your bootstrap distribution of t statistic.

b) Perform a t test to verify that the mean sales differ between the two programs. Use the level of

significance of 0.05. Must state your 1) hypotheses 2) test statistic 3) rejection region 4) test result in

the context of the situation.

c) Construct a 95% confidence interval of the mean sales difference. Accor

ding to the confidence interval, which program should the company adopt (with higher amount of sales)?

Solution