One of the major measures of the quality of service provided byany organization is the speed with which it responds to customercomplaints. A large family-held department store selling furnitureand flooring, including carpet, had undergone a major expansion inthe past several years. In particular, the flooring department hadexpanded from 2 installation crews to an installation supervisor, ameasurer, and 15 installation crews. The store had the businessobjective of improving its response to complaints. The variable ofinterest was defined as the number of days between when thecomplaint was made and when it was resolved. Data were collectedfrom 50 complaints that were made in the past year with sample mean43.04 and sample standard deviation 41.9261.
a. The installation supervisor claims that the mean number ofdays between the receipt of a complaint and the resolution of thecomplaint is 19 days. At the 0.01 level of significance, is thereevidence that the claim is not true (i.e., the mean number of daysis different from 19)?
b. What assumption about the population distribution is neededin order to conduct the t test in (a)?
