A hospital administrator has been asked by her supervisor to assess whether waiting time in the emergency room (ER) has changed from last year, when average wait time was 127 minutes. The administrator collects a simple random sample of 64 patients and records the time between when they checked in at the ER until they were first seen by a doctor; the average wait time is 137 minutes, with standard deviation 39 minutes.

a) Compute and interpret a 95% confidence interval for mean ER wait time at the hospital. Based on the interval, is mean ER wait time statistically significantly different from 127 minutes at the α = 0.05 level?

b) Would the conclusion in part a) change if the significance level were changed to α = 0.01?

c) Suppose that upon seeing the results from part a), the supervisor criticizes the hospital administrator on the basis that ER wait times have increased greatly from last year and the administrator must be at fault. Present a brief argument in favor of the administrator.