1. Jim owns his own burger restaurant. On some days he posts a sign that advertises his special Jimbuger, and on other days he does not. Jim has been collecting data on Jimburger sales for the past 70 days, with the following results:

For 38 of those days, Jim posted his Jimburger advertisement; the mean unit sales were 89 with a standard deviation of 17.

For 32 of those days, Jim did not post the advertisement; the mean unit sales were 77 with a standard deviation of 15.

a. If we treat the 70 days Jim collected data as a random sample, and if Jim randomly chose when to advertise, what is the distribution of the difference between mean unit sales when advertising and mean unit sales when not advertising?

b. Suppose Jim believed that the advertisement was responsible for an increase in sales of Jimburgers by 20 burgers. Do these data support or reject this hypothesis?

2. A regional Internet service provider (ISP) is interested in whether a 15% discount on its price for its highest-speed service will notably impact customer retention. To answer this question, the ISP randomly chooses 75 of the 150 markets it serves to receive the 15% discount, and keeps prices the same in the remaining 75 markets. After six months, the ISP observes the following: (LO4)

For the markets receiving the discount, the average retention rate was 0.93 (i.e., 93%), with a standard deviation of 0.255.

For the markets not receiving the discount, the average retention rate was 0.88, with a standard deviation of 0.325.

Using a 95% confidence interval, determine whether you can state with 95% confidence that the discount improved the six-month retention rate.