One of the major measures of the quality of service provided by an organization is the speed by which it responds to customer complaints. A large family-held department store selling furniture and flooring, including carpet, had undergone a major expansion in the past several years. In particular, the flooring department had increased the number of installation crews, with the objective of improving its response to complaints. The variable of interest was defined as the number of days between when the complaint was made and when it was resolved. The data collected from 64 complaints made in the past year shows an average number of days X-bar = 40 days, and a sample standard deviation s = 20 days.

Construct a 95% confidence interval for the population mean number of days between the receipt of a complaint and the resolution of the complaint.

The sales department is promising they can resolve complaints in fewer than 38 days. According to your results in a), is that a reasonable claim? Why?

A consultant is now hired to improve the operational processes of the department store, and would like to conduct a follow-up study. What sample size would be required to estimate the number of days needed to resolve a complaint with 95% confidence level and an error of +/- 3 days? Assume the standard deviation of the population is equal to 22 days.