Problem 2 (1 point each): To increase business, the owner of a restaurant is running a promotion in which a customer's bill can be randomly selected to receive a discount. When a customer's bill is printed, a program in the cash register randomly determines whether the customer will receive a discount on the bill. The program was written to generate a discount with a probability of 0.15, that is, giving 15 percent of the bills a discount in the long run. However, the owner is concerned that the program has a mistake that results in the program not generating the intended long-run proportion of 0.15. The owner selected a random sample of bills and found that only 10 percent of them received discounts. A condence interval for p, the proportion of bills that will receive a discount in the long run, is 0.10 i 0.07. Assume all conditions for inference were met. a. Does the condence interval provide convincing statistical evidence that the program is not working as intended? b. Does the condence interval provide convincing statistical evidence that the program generates the discount with a probability of 0.15? c. A second random sample of bills was taken that was four times the size of the original sample. In the second sample 10 percent of the bills received the discount. The new interval is 0.10 i 0.035. What do you conclude about whether the program is working as intended