An appliance manufacturer stockpiles washers and dryers in a large warehouse for shipment to retail stores. Some appliances get damaged in handling. The long-term goal has been to keep the level of damaged machines below 2%. In a recent test, an inspector randomly checked 60 washers and discovered that 5 of them had scratches or dents. Test the null hypothesis H0: p ≤ 0.02 in which p represents the probability of a damaged washer.
(a) Do these data supply enough evidence to reject H0? Use a binomial model from Chapter 11 to obtain the p-value.
(b) What assumption is necessary in order to use the binomial model for the count of the number of damaged washers?
(c) Test H0 by using a normal model for the sampling distribution of p̂. Does this test reject H0?
(d) Which test procedure should be used to test H0? Explain your choice.