HW 11 Key

16:39 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.

16:39 a Do these data supply enough evidence to reject H0? Use a binomial model to obtain the p-value. Yes, the p-value is P(X>=5) ~.007, which reject H0 for alpha=.05.

16:39 a and c calculations

16:39 a and c calculations

16:39 a and c calculations

16:39 b b. What assumption is necessary in order to use the binomial model for the count of the number of damaged washers? Inspection must produce independent outcomes with constant chance p for finding a defect.

16:39 c c. Test H0 by using a normal model for the sampling distribution of p^. Does this test reject H0? z~3.5>1.645 standard errors above H0. Reject H0 for alpha alpha=.05.

16:39 d d. Which test procedure should be used to test H0? Explain your choice. The expected number of events is too small. Use binomial methods.

16:43 The management of a chain of hotels avoids interviewing in the local management of its franchises unless problems become far too common to ignore. Management believes that solving the problems is better left to the local staff unless the measure of satisfaction drops below 33%. A survey of 80 guests who recently stayed in the franchise in St Louis found that only 20% of the guests indicated that they would return to that hotel when next visiting the city. Should management intervene in the franchise in St Louis?

16:43 a. State the null and alternative hypotheses. H0:p>=.33 versus Ha:p<.33; p is the proportion of all visitors who will indicate a willingness to return.

16:43 b b. Describe Type I and Type II errors in this context. A Type I error implies concluding that loyal shoppers spend more when they do not (incorrectly reject H0). A Type II error occurs if we fail to reject H0 when it’s false, missing the opportunity to correct a problem.

16:43 c c. Find the p value of the test. Do the data supply enough evidence to reject the null hypothesis if alpha=.025? Approximately P(Z<-2.53) = .0057. Yes.

16:43 c calculations