A manager of small store wanted to discourage shoplifters by putting signs around store saying "Shoplifting is a crime!" But, he wanted to ensure this would not result in customers buying less. To test this, he displayed the signs every other Wednesday for eight weeks, for a total of four days displayed. He recorded the store's sales for those four Wednesdays and then recorded the store's sales for four alternate Wednesdays, when the signs were not displayed. On the Wednesdays with sign, the sales were 83, 73, 81, and 79. On the Wednesdays without the sign, sales were 84, 90, 82, and 84.
Do these results recommend that customers purchase less when the signs are displayed? (To figure this out, use the .05 significance level and work through the steps below.)
NOTE: This is a t-test problem and you will require figuring out the S2Pooled and S2Difference for this type of t-test.
a. Employ the five steps of hypothesis testing.
b. Figure out the effect size.
c. Discuss what you did to a person who is familiar with the t test for single sample but is unfamiliar with the t test for independent means.