A hospital has a main campus and three satellite locations. Management wants to
ID: 3245760 • Letter: A
Question
A hospital has a main campus and three satellite locations. Management wants to reduce waiting time for ER cases. A random sample of 11 ER cases at each location were selected, and the waiting time was measured.
Complete parts (a) through (c).
Main Sate_1 Sate_2 Sate_3
73.80 42.46 25.26 46.09
58.18 69.14 58.77 20.77
89.64 52.20 49.47 38.18
67.15 36.39 45.27 28.93
75.90 75.87 37.82 55.25
94.16 49.92 47.87 32.18
63.38 60.21 60.96 57.43
59.52 83.00 35.57 48.82
78.14 76.48 33.95 40.63
46.02 45.20 57.13 44.05
41.35 68.26 69.50 65.71
Critical values of the Studentized Range, Q. Upper 5% points (alpha=0.05).
Numerator, df
Denominator, df 2 3 4 5 6 7 8 9 10
1 17.97 26.98 32.82 37.08 40.41 43.12 45.40 47.36 49.07
2 6.09 8.33 9.80 10.88 11.74 12.44 13.03 13.54 13.99
3 4.50 5.91 6.83 7.50 8.04 8.48 8.85 9.18 9.46
4 3.93 5.04 5.76 6.29 6.71 7.05 7.35 7.60 7.83
5 3.64 4.60 5.22 5.67 6.03 6.33 6.58 6.80 7.00
6 3.46 4.34 4.90 5.31 5.63 5.90 6.12 6.32 6.49
7 3.34 4.17 4.68 5.06 5.36 5.61 5.82 6.00 6.16
8 3.26 4.04 4.53 4.89 5.17 5.40 5.60 5.77 5.92
9 3.20 3.95 4.42 4.76 5.02 5.24 5.43 5.60 5.74
10 3.15 3.88 4.33 4.65 4.91 5.12 5.31 5.46 5.60
11 3.11 3.82 4.26 4.57 4.82 5.03 5.20 5.35 5.49
12 3.08 3.77 4.20 4.51 4.75 4.95 5.12 5.27 5.40
13 3.06 3.74 4.15 4.45 4.69 4.89 5.05 5.19 5.32
14 3.03 3.70 4.11 4.41 4.64 4.83 4.99 5.13 5.25
15 3.01 3.67 4.08 4.37 4.60 4.78 4.94 5.08 5.20
16 3.00 3.65 4.05 4.33 4.56 4.74 4.90 5.03 5.15
17 2.98 3.63 4.02 4.30 4.52 4.71 4.86 4.99 5.11
18 2.97 3.61 4.00 4.28 4.50 4.67 4.82 4.96 5.07
19 2.96 3.59 3.98 4.25 4.47 4.65 4.79 4.92 5.04
20 2.95 3.58 3.96 4.23 4.45 4.62 4.77 4.90 5.01
24 2.92 3.53 3.90 4.17 4.37 4.54 4.68 4.81 4.92
30 2.89 3.49 3.85 4.10 4.30 4.46 4.60 4.72 4.82
40 2.86 3.44 3.79 4.04 4.23 4.39 4.52 4.64 4.74
60 2.83 3.40 3.74 3.98 4.16 4.31 4.44 4.55 4.65
120 2.80 3.36 3.69 3.92 4.10 4.24 4.36 4.47 4.56
infinity 2.77 3.31 3.63 3.86 4.03 4.17 4.29 4.39 4.47
a. At the 0.05 level of significance, is there evidence of a difference in the mean waiting times in the four locations?
Determine the hypotheses. Choose the correct answer below.
A. H0: 1 = 2 = • • • =4; H1: Not all jj are equal (where j =1,2,...,4)
B. H0: 1 = 2 = • • • = 11; H1: 1 2 • • • 11
C. H0: 1 = 2 = • • • = 11; H1: Not all jj are equal (where =1,2,...,11)
D. H0: 1 = 2 = • • • = 4; H1: 1 2 • • • 4
Find the test statistic.
FSTAT = ____? (Round to two decimal places as needed.)
Find the p-value.
p-value = ____? (Round to three decimal places as needed.)
Since the p-value is (less, greater) than , (do not reject, reject) H0. There is (sufficient, insufficient) evidence to conclude that there is a difference in the mean waiting time in the four locations.
b. If appropriate, determine which locations differ in mean waiting time. At the 0.05 level of significance, for which locations is there enough evidence to conclude that the mean waiting time differs? Select all that apply.
___A. Satellite 1 and satellite 3 differ in mean waiting time.
___B. The main campus and satellite 3 differ in mean waiting time.
___C. Satellite 1 and satellite 2 differ in mean waiting time.
___D. The main campus and satellite 1 differ in mean waiting time.
___E. The main campus and satellite 2 differ in mean waiting time.
___F. The Tukey-Kramer procedure is not appropriate
c. At the 0.05 level of significance, is there evidence of a difference in the variation in waiting time among the four locations?
Determine the hypotheses. Choose the correct answer below.
A. H0: 1 = 2 = • • • = 11; H1: Not all jj are equal (where jequals=1,2,...,11)
B. H0: 1 = 2 = • • • = 4; H1: 1 2 • • • 4
C. H0: 1 = 2 = • • • = 4; H1: Not all jj are equal (where j = 1,2,...,4)
D. H0: 1 = 2 = • • • = 11; H1: 1 2 • • • 11
Find the test statistic.
FSTAT = ____? (Round to two decimal places as needed.)
Find the p-value.
p-value = ____? (Round to three decimal places as needed.)
Since the p-value is (greater, less) than , (reject, do not reject) H0. There is (sufficient, insufficient) evidence to conclude that there is a difference in the variation in waiting time in the four locations
Explanation / Answer
I have done the ANOVA analysis here so the result is
a. The correct hypothesises are
A. H0: 1 = 2 = • • • =4; H1: Not all jj are equal (where j =1,2,...,4)
so option A is correct.
F- stat = 6.40
p - vlaue = 0.0012
so as p- value is less than 0.05 so we can reject the null hypotheis.There is sufficient evidence to conclude that there is a difference in the mean waiting time in the four locations.
b. Tukey Cramer procedure for each group of means
HEre is the difference in mean teable
THe Q value for each pairwise comparison
formula is
Q = (M1 - M2)/ sqrt (MSW/n)
Critical Q value = 3.79
so the pair of means which differs are Main satellites and Satellite 1 and Satellite 2. So, option B and E are correct.
c. We have to check that variance are equal or not for all the four locations.
so hypothesises are
C. H0: 1 = 2 = • • • = 4; H1: Not all jj are equal (where j = 1,2,...,4) OPtion C is correct.
Anova: Single Factor SUMMARY Groups Count Sum Average Variance Main 11 747.24 67.93 273.52 Sate_1 11 659.13 59.92 245.08 Sate_2 11 521.57 47.42 180.81 Sate_3 11 478.04 43.46 175.43 ANOVA Source of Variation SS df MS F P-value F crit Between Groups 4199.32 3 1399.77 6.40 0.00 2.84 Within Groups 8748.35 40 218.71 Total 12947.67 43Related Questions
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