10.45 Most retail outlets like H&M, Zara, and Forever21 have an end-of-season sale in December every year.

Suppose the manager of a retail chain in Arezzo, Italy, wants to know the sales for two outlets and determine the difference in sales between them. The sales report showed that outlet 1 located at a prime shopping area had a 45% increment in its sales during December one year. Outlet 2, which was located in a residential area, also had an increment of 40% during the December sales. From outlet 1, 275 entries out of a total sample of 534 entries in the sales report indicated purchases of discounted items. From outlet 2, 242 out of a total sample of 421 entries indicated purchases of discounted items.

a. Using a probability of error a = 0.06, test the hypothesis that the proportion of purchasing discounted items are equal versus the hypothesis that they are not equal (outlet 2 – outlet 1).

b. Using a probability of error a = 0.06, test the hypothesis that the proportion of purchasing discounted items are equal versus the hypothesis that the proportion of purchasing discounted items in outlet 2 is larger.