The psychologist's theory suggests that we should not expect any difference on average between discount and standard sales. This is the null hypothesis we want to test.

The mean observed difference is Y=-69. The standard error of Y is given by SE(Y)=150/(60^(1/2))=19.36. The two sample z-statistic is z=( observed difference - expected difference ) / ( SE for difference ) = -69/19.36 = -3.563.

In other words the difference between discount and standard sales is about 3.5 SE's below the value expected under the null hypothesis. Hence, we reject the null hypothesis and accept the alternative hypothesis that the difference is real.

Remarks:

  1. The test assumes simple random samples, which is the case here.
  2. The sample is large enough so due to the Central Limit Theorem the probability histogram for each sample average and consequently of their difference follows the normal curve.

The pairing of the stores according to sales volume, location etc allows us to compare similar things and eliminates from the test procedure potential confounding factors.