AP Statistics · Unit 7 · Inference for Quantitative Data: Means

A university housing office manages on-campus apartments for undergraduate and graduate students. When a resident submits a maintenance request (for example, a leaking faucet or a broken heater), a work order is logged and closed once the repair is completed. The housing office's public materials state that the mean time to resolve a maintenance request is 2.5 days, but some resident advisors suspect requests actually take longer than the office claims.

To investigate, a staff member selected a random sample of 28 maintenance requests from the university's database of 900 requests submitted during the past academic year. For each selected request, the number of days between submission and resolution was recorded. A boxplot of the 28 resolution times was fairly symmetric with no outliers. Summary statistics are shown below.

Let $\mu$ represent the true mean resolution time, in days, for all maintenance requests submitted by residents of this university's on-campus housing during the past academic year.

(a) Do these data provide convincing statistical evidence, at $\alpha = 0.05$, that the true mean resolution time is greater than 2.5 days? Carry out an appropriate test, using the critical value $t^{*} = 1.703$ ($df = 27$).
(b) Can the conclusion from part (a) be generalized to maintenance requests at housing offices of other universities? Explain, based on how the sample was obtained.