Question

The following shows the monthly sales in units of six salespersons before and after a bonus plan was introduced. At 95% confidence, determine whether the bonus plan has increased sales significantly. (For the following matched samples, let d = After – Before.)

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

Sample Mean of d (d) = 3

Sample Standard Deviation (sd) = 3.58

Answer 1

The given table shows the monthly sales in units of six salespersons before and after a bonus plan was introduced.

At alpha = 5 %, i.e. at 5% level of significance we want to check the hypothesis that ' whether the bonus plan has increased sales significantly ' i.e. to test

H0: μd = 0

vs

H1: μd  > 0

( given d = After - Before )

Given : = 3 , sd of d = 3.58 and n = 6

t0.05,5 = 2.015048 ( table value )

tcal = 2.0526 ( using above formula )

Hence reject H0 since  tcal > t0.05,5 at 95% confidence.

So, we can conclude that the bonus plan has increased sales significantly.