Question

Suppose that the average waiting time for a patient at a physician's office is just over 29 minutes. In order to address the issue of long patient wait times, some physicians' offices are using wait-tracking systems to notify patients of expected wait times. Patients can adjust their arrival times based on this information and spend less time in waiting rooms. The following data show wait times (minutes) for a sample of patients at offices that do not have a wait-tracking system and wait times for a sample of patients at offices with a wait-tracking system.

Without Wait- Tracking System	With Wait-Tracking System
20	8
56	12
12	11
35	16
26	32
48	36
16	8
10	9
27	15
36	5

(a)	Considering only offices without a wait-tracking system, what is the z-score for the 10th patient in the sample (wait time = 36 minutes)?
	If required, round your intermediate calculations and final answer to two decimal places.
	z-score =
(b)	Considering only offices with a wait-tracking system, what is the z-score for the 6th patient in the sample (wait time = 36 minutes)?
	If required, round your intermediate calculations and final answer to two decimal places.
	z-score =
	How does this z-score compare with the z-score you calculated for part (a)?
	The input in the box below will not be graded, but may be reviewed and considered by your instructor.
(c)	Based on z-scores, do the data for offices without a wait-tracking system contain any outliers?
	- Select your answer -YesNoItem 4
	Based on z-scores, do the data for offices with a wait-tracking system contain any outliers?

Answer 1

Z-score of a value is computed in the following way: .
The table below consists the z-scores and the original values of the waiting times.

without wait tracking systems	with wait tracking systems	Z score of without wait tracking systems	Z score of with wait tracking systems
20	8	-0.56	-0.69
56	12	1.80	-0.31
12	11	-1.09	-0.40
35	16	0.42	0.08
26	32	-0.17	1.60
48	36	1.27	1.98
16	8	-0.83	-0.69
10	9	-1.22	-0.59
27	15	-0.11	-0.02
36	5	0.49	-0.97

(a) From the table above, we can see that the z-score for the 10th patient in the sample (wait time = 36 minutes) is = 0.49.
In this case, mean (of without wait tracking systems) was 28.6 and s.d. (of without wait tracking systems) was 15.226.

(b) From the table above, we can see that the z-score for the 6th patient in the sample (wait time = 36 minutes) is = 1.98.
In this case, mean (of with wait tracking systems) was 15.2 and s.d. (of with wait tracking systems) was 10.486.

The z-score of part(b) is higher than the z-score in part(a). This is because the corresponding mean in part(b) is much lower than the corresponding mean in part(a).

(c) Based on z-scores, neither the data for offices without a wait tracking system nor the data for offices with a wait tracking system contain any outliers.