One of the major measures of the quality of service provided by an 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 complaint was made and when it was resolved. Data were collected from 25 complaints that were made in the past year. The mean number of days between complaints made and resolved is 43.04 with a standard deviation of 21.9 days.
The installation supervisor claims that the mean number of days between the receipt of a compliant and the resolution of the compliant is 30 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 30)?