One of the major measures of the quality of service provided by any organization is the speed with 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 expanded from 2 installation crews to an installation supervisor, a measurer, and 15 installation crews. The store had the business 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. Data were collected from 30 complaints that were made in the past year as follows (you can also find the data in furniture.xlsx):

54 5 35 137 31 27 152 2 123 81 74 27 11 19 126 110 110 29 61 35 94 31 26 5 12 4 165 32 29 28 29 26 25 1 14 13 13 10 5 27

(a) The installation supervisor claims that the mean number of days between the receipt of a complaint and the resolution of the complaint is 20 days. At the 0.05 level of significance, is there evidence that the claim is not true? (i.e. the mean number of days is different from 20)?

(b) What assumption about the population distribution is needed in order to conduct the t-test in (a)?

(c) Construct a boxplot or a normal probability plot to evaluate the assumption made in (b).

(d) Do you think that the assumption needed in order to conduct the t-test in (a) is valid? Explain.