Question

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?

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

3. 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.

Answer 1

(a)

137.00	mean 1
39.00	std. dev.
4.88	std. error
64	n
63	df
127.26	confidence interval 95.% lower
146.74	confidence interval 95.% upper
9.74	margin of error

The 95% confidence interval for mean ER wait time at the hospital is between 127.26 and 146.74.

Since 127 is not in the confidence interval, we can say that the mean ER wait time is statistically significantly different from 127 minutes at the α = 0.05 level.

(b)

137.00	mean 1
39.00	std. dev.
4.88	std. error
64	n
63	df
124.05	confidence interval 99.% lower
149.95	confidence interval 99.% upper
12.95	margin of error

The 99% confidence interval for mean ER wait time at the hospital is between 124.05 and 149.95.

Yes, the conclusion in part a) would change if the significance level was changed to α = 0.01 since 127 is in the confidence interval.

(c) Since the mean ER wait time at the hospital from the part a) is above 127 minutes, we can support the administrator's claim that the ER wait times have increased greatly from last year.