Question

The following table shows the monthly sales (in units) of six salespersons before and after a bonus plan was introduced. Using α = .05, determine whether the bonus plan has increased sales significantly. Assume the population of differences is normally distributed. (For the following matched samples, let the difference d = After - Before.)

	Monthly Sales
Salesperson	After	Before
1	90	90
2	82	80
3	85	84
4	76	84
5	94	70
6	79	80

What would be an appropriate alternative hypothesis?

a. The population mean of the differences is 0

b. The population mean of the differences is not equal to 0

c. The population mean of the differences is greater than 0

d. The population mean of the differences is less than 0

Choose an answer from a-d:

What is the value of dbar =  and sd=  Round to three decimal places.

What would be the correct test statistic if you were running a paired t-test? Round to three decimal places.

How many df do we use in this test?

What would be the correct p-value? Round to four decimal places.

What is the correct conclusion?

We will (choose one: reject/fail to reject)  the null hypothesis. There (choose one: is/is not)  enough evidence to suggest that there is an increase in the mean monthly sales before and after a bonus plan was introduced.

Answer 1

(a) Alternative hypothesis

c. The population mean of the differences is greater than 0

(b) Test statistics

Store	Before	After	Diff (Af-Bef)	Dev (diff - mean)	Sq deviation
1	90	90	0	-3.0	9.0
2	80	82	2	-1.0	1.0
3	84	85	1	-2.0	4.0
4	84	76	-8	-11.0	121.0
5	70	94	24	21.0	441.0
6	80	79	-1	-4.0	16.0
Total	488	506	18.0	0.0	592.0

dbar = 18/ 6 = 3

d bar = 3

sd = 10.881

t stat = 0.675

df = 6-1= 5

p value = TDIST(0.675, 0.05, 1) = 0.2647

p value = 0.2647

As the p value (0.2647) is greater than 0.05, we fail to reject the Null hypothesis.

We will fail to reject the null hypothesis. There is not enough evidence to suggest that there is an increase in the mean monthly sales before and after a bonus plan was introduced.