Question

Solution needed in excel file.

A hospital conducted a study of the waiting time in its emergency room. The hospital has a main campus a three affiliated 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 and stores in ERWaiting (see folder). At the 0.05 level of significance, is there evidence of a difference in the mean waiting times in the four location?

Main	Satellite 1	Satellite 2	Satellite 3
120.08	30.75	75.86	54.05
81.90	61.83	37.88	38.82
78.79	26.40	68.73	36.85
63.83	53.84	51.08	32.83
79.77	72.30	50.21	52.94
47.94	53.09	58.47	34.13
79.88	27.67	86.29	69.37
48.63	52.46	62.90	78.52
55.43	10.64	44.84	55.95
64.06	53.50	64.17	49.61
64.99	37.28	50.68	66.40
53.82	34.31	47.97	76.06
62.43	66.00	60.57	11.37
65.07	8.99	58.37	83.51
81.02	29.75	30.40	39.17

Answer 1

Solution:

We can use the excel ANOVA: Single Factor data analysis tool to find the answer to the given questions.
The excel steps are:

Enter the data in excel.

Click on Data > Data Analysis > ANOVA: Single Factor > OK

Input Range: Select the data range for all the data including labels

Mark Labels in the first row

Alpha = 0.05

Choose the output range and click OK.

The output is given below:

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance
Main	15	1047.64	69.8427	331.3198
Satellite 1	15	618.81	41.2540	375.9760
Satellite 2	15	848.42	56.5613	205.3533
Satellite 3	15	779.58	51.9720	408.2862
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	6312.4439	3	2104.1480	6.3717	0.0009	2.7694
Within Groups	18493.0937	56	330.2338
Total	24805.5375	59

The null and alternative hypotheses are:

The test statistic is:

The p-value is:

Conclusion: Since the p-value is less than the significance level, we, therefore, reject the null hypothesis and conclude that there is sufficient evidence to support the claim that there is a difference in the mean waiting times in the four locations at the 0.05 significance level.