Question

use graph D and E to find mean of each service type(1,2,3,4)

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Col. B Column A Col D Col. E Col. G Sample: elapsed Type of times service before process changed Urgent Care facility Sample: patient times in elapsed minutes, collected on 2 successive times after process days improved 65 49 33 49 147 147 50 38 190 190 78 4 55 200 179 200 90 90 47 45 90 97 97 24 45 95 93 42 30 95 6 30 125 111 125 46 80 49 57 30 58 143 143 47 33 61 47 38 22 38 78 78 90 48 179 97 179 75 4. 95 33 47 30 24 30 24 93 125 70 95 04 11 54 111 143 111 57 80 90 80 57 30 240 30 30 6 99 24 55 22 22 270 22 66 120 56 90 58 150 240 166 240 56 99 130 55 270 56 95 270 120 120 30 47 150 48 150 125 3 166 11 166 59 130 143 130 54 156 30 156 57 48 136 61 136 178 22 178 49 56 146 66 146 245 90 245 52 240 243 243 55 124 99 30 124 36 92 92 270 55 88 120 50 75 150 75 42 45 65 166 1 11 Question 1 (20 points) Using a level of significance of a-0.05, test whether the means of the four types of services are equal. Assume the samples for the four types were independently drawn and that the four populations are normally distributed Question 2 (20 points) Compare the sample standard deviations of the four types of service.

Answer 1

Solution Q1 comparison of mean of 4 types of service.

Solution is based on One-way ANOVA with unequal number of observations per group.

Final Results

ANOVA	Table	alpha	0.05
Source	DF	SS	MS	F	Fcrit	p-value
Shift	3	136317	45438.9	52.61132	2.845068	8.936E-14
Error	39	33683	863.6717
Total	42	170000	4047.617

Since F > Fcrit or equivalently, since p-value < alpha, null hypothesis of equal means is rejected.

Hence, we conclude that the means of 4 types of Services are NOT equal. Answer

DONE

Details

Data

Ser 1	Ser 2	Ser 3	Ser 4
61	90	147	190
49	97	125	200
47	95	93	143
38	78	95	179
33	80	120	111
30	66	150	240
30	90	166	270
24	99	130	156
22	92	136	178
11	88	124	146
65	75		245
			243

Calculations

alpha	0.05
#treat	4
n1	10	n4	12
n2	11
n3	10
n	43
x1.	410	x4.	2301
x2.	950
x3.	1286
G = x..	4947
C	569135.093
Sx1j^2	18070	Sx4j^2	467821
Sx2j^2	83108
Sx3j^2	170136
Sxij^2	739135
Sxi.^2/ni	705451.8045
SST	169999.907
SSR	136316.7115
SSE	33683.19545

DONE