Question

At ABC department store they wish to investigate the effect of assisting trained sales people in
the store on sales. They believe that the sales will be less if there was no trained sales people in
the shop to help customers around. To test that claim, they recorded mean sales over a period of
15 days with no assisting sales people in the store, and then recorded mean sales over 14 days
with assisting sales people around the store. The results were recorded in the below table:

No assisting sales people in
the store (1)

With assisting sales people
around the store (2)

Sample standard deviation s1 = $500 s2 = $600
Sample Mean sales x̄1 = $5,000 x̄2 = $5,500
Sample size (days) n1 = 15 n2 = 14
Assume that random samples came from normal population with equal standard
deviations.
At the 0.025 (2.5%) significance level, can it be concluded that the mean sales with no assisting
sales people is less than the mean sales with assisting sales people available around the store?
a. Use 5 steps Hypothesis testing.
b. Confirm your answer using the P-value method.

Answer 1

a) As we are testing here whether the mean sales with no assisting sales people is less than the mean sales with assisting sales people available around the store, therefore this is a case of test of difference in means.

The standard error here is computed as:

Now as this is a test for difference in means, therefore the test statistic here is computed as:

Now as this is a one tailed test, for n₁ + n₂ - 2 = 27 degrees of freedom, we have from the t distribution tables here:
P( t₂₇ < -2.052) = 0.025

As the test statistic value here is -2.43 < -2.052 which is the critical value for the test, therefore the test is significant and we can reject the null hypothesis here. Therefore we have sufficient evidence here that the mean sales with no assisting
sales people is less than the mean sales with assisting sales people available around the store

b) For 27 degrees of freedom, we have from the t distribution tables here:

P( t₂₇ < -2.43) = 0.0110

As the p-value here is 0.0110 < 0.025 which is the level of significance, therefore the test is significant and we can reject the null hypothesis here. Therefore we have sufficient evidence here that the mean sales with no assisting
sales people is less than the mean sales with assisting sales people available around the store