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.