Question

A hospital conducts a study of the waiting times in its emergency room. The hospital has a main campus nd three satellite locations. Management had a business objective of reducing waiting time for emergency room cases that did not require immediate attention.To study this, a random sample of 15 emergency room cases that did not require immediate attention at each location were selected on a particular day, and the waiting times (measured from check-in to when the patient was called into the clinic area) were collected.

a. At a 0.05 level of significance, is there evidence of a difference in the mean waiting times in the locations

b. If appropriate, determine which locations differ in mean waiting times

c. At the 0.05 level of significance, is there evidence of a difference in the variation in waiting time among the four locations?

Location_A	WaitTime
1	120.080
1	81.900
1	78.790
1	63.830
1	79.770
1	47.940
1	79.880
1	48.630
1	55.430
1	64.060
1	64.990
1	53.820
1	62.430
1	65.070
1	81.020
2	30.750
2	61.830
2	26.400
2	53.840
2	72.300
2	53.090
2	27.670
2	52.460
2	10.640
2	53.500
2	37.280
2	34.310
2	66.000
2	8.990
2	29.750
3	75.860
3	37.880
3	68.730
3	51.080
3	50.210
3	58.470
3	86.290
3	62.900
3	44.840
3	64.170
3	50.680
3	47.970
3	60.570
3	58.370
3	30.400
4	54.050
4	38.820
4	36.850
4	32.830
4	52.940
4	34.130
4	69.370
4	78.520
4	55.950
4	49.610
4	66.400
4	76.060
4	11.370
4	83.510
4	39.170

Answer 1

Solution :

Using Excel<data<data analysis<anova one way

Here is the screenshot

Here is the output :

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Main	15	1047.64	69.84267	331.3198
Satellite 1	15	618.81	41.254	375.976
Satellite 2	15	848.42	56.56133	205.3533
Satellite 3	15	779.58	51.972	408.2862
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	6312.444	3	2104.148	6.371691	0.000859	2.769431
Within Groups	18493.09	56	330.2338
Total	24805.54	59

a)

The hypothesis being tested is:

H0: µ1 = µ2 = µ3 = µ4

Ha: At least one means is not equal

Since the P-value is 0.001 which is less than the significance level 0.05. Thus, we reject the null hypothesis.

There is sufficient evidence to conclude that there is a significant difference between the mean waiting times at four locations.

b)

Groups	Average
Main	69.84267
Satellite 1	41.254
Satellite 2	56.56133
Satellite 3	51.972

There is a significant difference between mean waiting times of main and satellite 1 locations and between mean waiting times of main and satellite 3 locations.

c)

F-critical value for (3,56) is 2.7694

Since F(6.3717)>F critical value. We reject the null hypothesis. There is sufficient evidence in favor of significant differences among the variations in waiting times of four locations.

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