A manager of a small store wanted to discourage shoplifters by putting signs around the store that said, "Shoplifting is a crime!", while at the same time making sure the signs would not reduce the number of sales. To test the effect on sales, the signs were displayed every other Wednesday for 8 weeks, and the numbers of sales for those four Wednesdays were 83, 73, 81, and 79. The numbers of sales for the four alternate Wednesdays without the sign were 84, 90, 82, and 84. Using the .05 significance level, did customers make fewer purchases when the signs were displayed?
a. Use the five steps of hypothesis testing.
b. Sketch the distributions involved.
c. Figure the effect size.
d. Explain the logic of what you did to a person who is familiar with the t test for a single sample, but who is unfamiliar with the t test for independent means. Be sure you explain how this problem differs from a t test for a single sample. Your answer should consist mainly of a thorough explanation of the characteristics of the comparison distribution and the logic of all the steps of figuring you did to determine those characteristics.
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