Question

The monthly sales for six sales people before and after a bonus plan was introduced showed an after bonus sales average of 3 units higher than before the sales bonus average with a standard deviation of the difference being 3.5777.  At a 0.05 level of significance, test whether the bonus plan has significantly increased sales.

Answer 1

Here, we have to use paired t test.

The null and alternative hypotheses for this test are given as below:

H₀: µ_d = 0 versus H_a: µ_d > 0

This is a right tailed test.

Test statistic for paired t test is given as below:

t = (Dbar - µ_d)/[S_d/sqrt(n)]

From given data, we have

Dbar = 3

S_d = 3.5777

n = 6

df = n – 1 = 5

α = 0.05

t = (Dbar - µ_d)/[S_d/sqrt(n)]

t = (3 - 0)/[ 3.5777/sqrt(6)]

t = 2.0540

The p-value by using t-table is given as below:

P-value = 0.0476

P-value < α = 0.05

So, we reject the null hypothesis

There is sufficient evidence to conclude that the bonus plan has significantly increased sales.