Question
Asked Nov 21, 2019
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In a 1996 article published in Technometrics, 38, pp. 11–22, the authors discuss the reliability of nuclear power plant emergency generators. To control the risk of damage to the nuclear core during accidents at nuclear plants, the reliability of emergency diesel generators (EDG) to start on demand must be maintained at a very high level. At each nuclear power plant there are a number of such generators. An overall measure of reliability is obtained by counting the number of times the EDGs successfully work when needed. The table here provides the number of successful demands for implementation of an EDG between each subsequent failure in an EDG for all the EDGs at each of seven nuclear power plants. A regulatory agency wants to determine if there is a difference in the reliability of the seven nuclear power plants. (Use Data _8).

Run an ANOVA (Regardless of the assumptions) and Kruskal–Wallis test.

'A'
'B
'C
'D
E'
'F'
142
139
28
2
64
18
50
11
110
29
21
108
6
193
75
214
9
273
55
6
3
67
16
4
1
54
174
17
1
7
12
32
29
1
88
58
174
4
4
28
13
76
6
40
60
36
10
64
23
119
33
30
237
19
10
17
110
84
7
71
12
20
6
1
78
12
7
62
5
26
15
226
54
46
128
4
105
40
4
273
164
7
55
41
26
6
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'A' 'B 'C 'D E' 'F' 142 139 28 2 64 18 50 11 110 29 21 108 6 193 75 214 9 273 55 6 3 67 16 4 1 54 174 17 1 7 12 32 29 1 88 58 174 4 4 28 13 76 6 40 60 36 10 64 23 119 33 30 237 19 10 17 110 84 7 71 12 20 6 1 78 12 7 62 5 26 15 226 54 46 128 4 105 40 4 273 164 7 55 41 26 6

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Expert Answer

Step 1

Introduction:

The null and alternative hypotheses for both the tests are:

H0: There is no significant difference between the groups.

H1: At lest one of the groups has different effect than the others.

Step 2

ANOVA:

Enter the data in an Excel sheet, as given.

Choose Data > Data Analysis > Anova: Single Factor > OK.

Enter Input Range as $A$1:$G$35, choose Columns under Grouped by, tick on Labels and click OK.

The output is:

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Anova: Single Factor SUMMARY Variance Groups Count Sum Average A 34 1983 58.32352941 5095.255793 15 286 19.06666667 794.9238095 C 17 776 45.64705882 4943.367647 8 198 24.75 652.5 12 1164 97 6815.636364 7 276 39.42857143 1677.952381 G 10 182 18.2 362.1777778 ANOVA F crit Source of Variation df SS MS P-value Between Groups 58745.33662 6 9790.889436 2.676073135 0.019121234 2.194516205 Within Groups 351233.0711 96 3658.677824 Total 409978.4078 102

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Step 3

Kruskal-Wallis test:

In cell I2, enter the formula =RANK.AVG(A2,$A$2:$G$35,1).

Drag it along the column, as well as along the rows, to ensure that the rank of each observation is obtained.

Find the value of R, that is total group rank for each group.

Denote N as the total number of observations, n as the observation for a particular group.

The test statistic is obtained below:

H = [12/{N (N + 1)} Σ (R2/n)] – 3 (N + 1)

= 12/{(103) (104)} (289,694) – 3 (104) [Refer to the calculation shown below in the screenshot of the...

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P G H 78.5 42 89s 17 28 102.5 12 9.5 71.5 35.S 22 32.5 63 60.5 44 965 22 17 83 2 665 a0.s 75 22 26 4 3.5 7 62 325 85 17 35 95 44 38 3 28 9.5 84 44 3.5 32.5 77 56.5 71.5 69 92 22 87 22 102.5 95 32.5 73.5 68 56.5 345N 406 5 7 5315 15 3.5 350.5 1924.5 34 17 12 155630Sum (2/n 5542694 37037004 282492 798342 129240 715716 165242 RZ1/n 108932 188328 91.3 16355 55643 23606 3

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MathStatistics

Hypothesis Testing

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