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.

orchestra answered 2 years ago

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