Question

7. A hospital conducted a study of the waiting time in its emergency room. The hospital has a main campus and three satellite locations. Management has a business objective of reducing waiting time for emergency room cases that do 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 time (measured from check-in to when the patient was called into the clinic area) were collected and stored in ER.

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

b. Does the result in (a) give you statistical permission to probe for individual differences between hospital locations?

Main	Satellite 1	Satellite 2	Satellite 3
80.28	66.40	40.54	71.08
81.50	114.73	49.81	19.47
76.77	67.85	86.36	76.68
49.23	39.14	59.41	31.95
55.13	22.97	88.07	9.12
90.00	57.04	69.33	48.83
19.03	31.31	61.92	67.51
48.42	35.79	65.31	84.98
93.04	46.39	77.97	45.20
38.34	27.56	60.03	41.63
145.35	28.62	42.90	42.20
123.55	42.96	61.49	11.19
27.37	35.17	37.44	39.18
61.69	46.59	72.86	74.16
20.85	31.21	45.96	42.10

Answer 1

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

The hypothesis being tested is:

H0: µ1 = µ2 = µ3 = µ4

Ha: At least one means is not equal

	Mean	n	Std. Dev
	67.370	15	36.5246	Main
	46.249	15	23.3356	Satellite 1
	61.293	15	15.9206	Satellite 2
	47.019	15	23.7650	Satellite 3
	55.483	60	26.9134	Total
ANOVA table
Source	SS	df	MS	F	p-value
Treatment	4,979.6789	3	1,659.89296	2.46	.0719
Error	37,755.7051	56	674.20902
Total	42,735.3840	59

The p-value is 0.0719.

Since the p-value (0.0719) is greater than the significance level (0.05), we cannot reject the null hypothesis.

Therefore, we cannot conclude that there is a difference in the mean waiting times in the four locations.

b. Does the result in (a) give you statistical permission to probe for individual differences between hospital locations?

No, because there is no difference in the mean waiting times in the four locations.

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