Question

In: Statistics and Probability

A company attempts to evaluate the potential for a new bonus plan by selecting a sample...

A company attempts to evaluate the potential for a new bonus plan by selecting a sample of 4 salespersons to use the bonus plan for a trial period. The weekly sales volume before and after implementing the bonus plan is shown below. (For the following matched samples, let the difference "d" be d = after - before.)

Weekly Sales

Salesperson

Before

After

1

48

44

2

48

40

3

38

36

4

44

50

a. State the hypotheses.
b. Compute the test statistic.
c. Use Alpha = .05 and test to see if the bonus plan will result in an increase in the mean weekly sales.

Solutions

Expert Solution

Number After Before Difference
44 48 -4 4
40 48 -8 36
36 38 -2 0
50 44 6 64
Total 170 178 -8 104

To Test :-

H0 :-  

H1 :-  

Test Statistic :-





t = -0.6794


Test Criteria :-
Reject null hypothesis if


Result :- Fail to reject null hypothesis


Decision based on P value
P - value = P ( t > 0.6794 ) = 0.7272
Reject null hypothesis if P value < level of significance
P - value = 0.7272 > 0.05 ,hence we fail to reject null hypothesis
Conclusion :- Fail to reject null hypothesis

There is insufficient evidence to support the claim that the bonus plan will result in an increase in the mean weekly sales.


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