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
24	14
60	9
10	33
22	10
34	18
47	30
12	12
12	17
27	9
30	3

(a)	Considering only offices without a wait-tracking system, what is the z-score for the 10th patient in the sample (wait time = 30 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 = 30 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)?
(c)	Based on z-scores, do the data for offices without a wait-tracking system contain any outliers?
	Based on z-scores, do the data for offices with a wait-tracking system contain any outliers?

Answer 1

Solution:

In excel get the mean and standard deviation

Data>Data analysis>Descriptive statistics

we get

Without Wait-Tracking System		With-WaitTracking System
Mean	27.8	Mean	15.5
Standard Deviation	16.03329868	Standard Deviation	9.489761
Sum	278	Sum	155
Count	10	Count	10

Solution(a)

z=x-mean/sd

z=30-27.8/16.03329868

z=0.14

z score=0.14

Solution(b)

z=x-mean/sd

z=30-15.5/9.489761

z=14.5/9.489761

z= 1.527963

z=1.53

z score=1.53

z score for with wait tracking system is high compared to z score for without wait tracking system.

Solution(b)

with z score we can find outliers using z scores

outliers <-3 or outlier above 3

Without Wait-Tracking System	mean	stddev	X-mean	Z-x-mean/sd
24	27.8	16.0333	-3.8	-0.23701
60	27.8	16.0333	32.2	2.00832
10	27.8	16.0333	-17.8	-1.11019
22	27.8	16.0333	-5.8	-0.36175
34	27.8	16.0333	6.2	0.386695
47	27.8	16.0333	19.2	1.197508
12	27.8	16.0333	-15.8	-0.98545
12	27.8	16.0333	-15.8	-0.98545
27	27.8	16.0333	-0.8	-0.0499
30	27.8	16.0333	2.2	0.137214

With-WaitTracking System	Mean	Standard deviation	X-mean	z=x-mean/sd
14	15.5	9.489761	-1.5	-0.15807
9	15.5	9.489761	-6.5	-0.68495
33	15.5	9.489761	17.5	1.844093
10	15.5	9.489761	-5.5	-0.57957
18	15.5	9.489761	2.5	0.263442
30	15.5	9.489761	14.5	1.527963
12	15.5	9.489761	-3.5	-0.36882
17	15.5	9.489761	1.5	0.158065
9	15.5	9.489761	-6.5	-0.68495
3	15.5	9.489761	-12.5	-1.31721

no outliers  for offices without a wait-tracking system as no z value is below -3 or above 3

no outliers  for offices with a wait-tracking system as no z value is below -3 or above 3