Question

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.

Answer 1

a)

b)

we use Excel

data -> data analysis -> t-test : paired two sample for means

t-Test: Paired Two Sample for Means
	Before	After
Mean	44.5	42.5
Variance	22.33333333	35.66666667
Observations	4	4
Pearson Correlation	0.413369809
Hypothesized Mean Difference	0
df	3
t Stat	0.67936622
P(T<=t) one-tail	0.272813701
t Critical one-tail	2.353363435
P(T<=t) two-tail	0.545627401
t Critical two-tail	3.182446305

TS = -0.6794

c)

we fail to reject the null hypothesis

as TS < critical value 2.3533

P-Value = 0.727 > alpha

there is not sufficient evidence that bonus plan will result in an increase in the mean weekly sales.