Mathematical Statistics with Applications 477 52 16.56. Three groups of guinea p
ID: 3155580 • Letter: M
Question
Mathematical Statistics with Applications 477 52 16.56. Three groups of guinea pigs were injected, respec- tively, with 0.5, 1.0, and 1.5 milligrams of a tranquilizer and the following are the numbers of seconds it took them to fall asleep: 0.5-mg dose: 8.2 10.0 10.2 13.7 14.0 7.8 1.0-mg dose: 9.7 13.1 11.0 7.5 13.3 12.5 1.5-mg dose: 12.0 7.2 8.0 9.4 11.3 9.0 12.7 10.9 8.8 12.9 7.9 10.5 11.5 8.5 Use the H test at the 0.01 level of significance to test the null hypothesis that the differences in dosage have no effect on the length of time it takes guinea pigs to fall asleep.Explanation / Answer
Null hypothesis: Difference in dosages have no effect on the length of time it takes guinea pigs to fall asleep.
Alternate hypothesis: Difference in dosages have effect on the length of time it takes guinea pigs to fall asleep.
Calculated H statistic = 1.534
Critical value at 0.01 level =9.210
Calculated H statistic = 1.534 < 9.210 table value.
The null hypothesis is not rejected.
We conclude that the difference in dosages have no effect on the length of time it takes guinea pigs to fall asleep.
Kruskal-Wallis Test
Median
n
Avg. Rank
10.55
8
15.13
0.5mg
10.75
10
14.40
1.0mg
9.20
8
10.75
1.5mg
10.35
26
Total
1.534
H
2
d.f.
.4645
p-value
multiple comparison values for avg. ranks
8.80
(.05)
10.78
(.01)
No.
Label
Data
Rank
1
0.5mg
8.2
6
2
0.5mg
10
12
3
0.5mg
10
13
4
0.5mg
14
25
5
0.5mg
14
26
6
0.5mg
7.8
3
7
0.5mg
13
21
8
0.5mg
11
15
9
1.0mg
9.7
11
10
1.0mg
13
23
11
1.0mg
11
16
12
1.0mg
7.5
2
13
1.0mg
13
24
14
1.0mg
13
20
15
1.0mg
8.8
8
16
1.0mg
13
22
17
1.0mg
7.9
4
18
1.0mg
11
14
19
1.5mg
12
19
20
1.5mg
7.2
1
21
1.5mg
8
5
22
1.5mg
9.4
10
23
1.5mg
11
17
24
1.5mg
9
9
25
1.5mg
12
18
26
1.5mg
8.5
7
Kruskal-Wallis Test
Median
n
Avg. Rank
10.55
8
15.13
0.5mg
10.75
10
14.40
1.0mg
9.20
8
10.75
1.5mg
10.35
26
Total
1.534
H
2
d.f.
.4645
p-value
multiple comparison values for avg. ranks
8.80
(.05)
10.78
(.01)
No.
Label
Data
Rank
1
0.5mg
8.2
6
2
0.5mg
10
12
3
0.5mg
10
13
4
0.5mg
14
25
5
0.5mg
14
26
6
0.5mg
7.8
3
7
0.5mg
13
21
8
0.5mg
11
15
9
1.0mg
9.7
11
10
1.0mg
13
23
11
1.0mg
11
16
12
1.0mg
7.5
2
13
1.0mg
13
24
14
1.0mg
13
20
15
1.0mg
8.8
8
16
1.0mg
13
22
17
1.0mg
7.9
4
18
1.0mg
11
14
19
1.5mg
12
19
20
1.5mg
7.2
1
21
1.5mg
8
5
22
1.5mg
9.4
10
23
1.5mg
11
17
24
1.5mg
9
9
25
1.5mg
12
18
26
1.5mg
8.5
7