A new nail salon business just opened, in their first week ofbusiness they decided that thy would conduct a promotion in which acustomer's bill can be randomly selected to receive a discount.When a customer's bill is printed, a program in the cash registerrandomly determines whether the customer will receive a discount onthe bill. The program was written to generate a discount with aprobability of 0.2, that is, giving a discount to 20 percent of thebills in the long run. However, the owner is concerned that theprogram has a mistake that results in the program not generatingthe intended long-run proportion of 0.2.
(a) The owner selected a random sample of 100 bills and foundthat only 16 percent of them received discounts. The conditions forinference are met. Using the sample data collected by the owner,calculate a 95% confidence interval for the true proportion ofbills that will receive a discount in the long run.
(b) Observing the value that you received in part a. Do youbelieve that the confidence interval provide convincing statisticalevidence to indicate that the program is not working asintended?
