An experiment is conducted to investigate the toxic effect of three chemicals, A, B, and C on the skin of rats. Three adjacent 1-inch squares are marked on the backs of 8 rats and each of the 3 chemicals is applied to each rat. The squares of the skin are then scored from 0 to 10, depending on the degree of irritation. The data on the outcome of the experiment are given in the following table: Rat 1 A B C 6 5 3 9 8 4 6 9 3 5 8 6 7 8 9 5 7 6 7 5 7 2 3 4 5 6 7 6 8 6 5 Σε 150 157143 10 Rank A Rank B Rank C 11.5 6.0 1.5 23.0 20.0 3.0 11.5 23.0 1.5 6.0 20.0 11.5 16.5 20.0 23.0 6.0 16.5 11.5 11.5 16.5 6.0 11.5 6.0 16.5 For the original data set E-1-1=150, and Σ1-19 = 1006. From the ranks of the original data set the rank sums are RA = 97.5, RB 128, Rc = 74.5 respectively. At a 1%, is there sufficient evidence to support the research hypothesis that the probability distributions of skin irritation scores for the 3 chemicals differ in location? (a) Stating relevant hypotheses, test the above research hypothesis by using an appropriate nonparametric test. (b) Stating relevant hypotheses, test the above research hypothesis by using an appropriate parametric test. (c) In both of the above tests, state the underlying assumptions and discuss the differences in the assumptions for the two different tests.
An experiment is conducted to investigate the toxic effect of three chemicals, A, B, and C on the skin of rats. Three adjacent 1-inch squares are marked on the backs of 8 rats and each of the 3 chemicals is applied to each rat. The squares of the skin are then scored from 0 to 10, depending on the degree of irritation. The data on the outcome of the experiment are given in the following table: Rat 1 A B C 6 5 3 9 8 4 6 9 3 5 8 6 7 8 9 5 7 6 7 5 7 2 3 4 5 6 7 6 8 6 5 Σε 150 157143 10 Rank A Rank B Rank C 11.5 6.0 1.5 23.0 20.0 3.0 11.5 23.0 1.5 6.0 20.0 11.5 16.5 20.0 23.0 6.0 16.5 11.5 11.5 16.5 6.0 11.5 6.0 16.5 For the original data set E-1-1=150, and Σ1-19 = 1006. From the ranks of the original data set the rank sums are RA = 97.5, RB 128, Rc = 74.5 respectively. At a 1%, is there sufficient evidence to support the research hypothesis that the probability distributions of skin irritation scores for the 3 chemicals differ in location? (a) Stating relevant hypotheses, test the above research hypothesis by using an appropriate nonparametric test. (b) Stating relevant hypotheses, test the above research hypothesis by using an appropriate parametric test. (c) In both of the above tests, state the underlying assumptions and discuss the differences in the assumptions for the two different tests.
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Transcribed Image Text:An experiment is conducted to investigate the toxic effect of three chemicals, A, B,
and C on the skin of rats. Three adjacent 1-inch squares are marked on the backs
of 8 rats and each of the 3 chemicals is applied to each rat. The squares of the skin
are then scored from 0 to 10, depending on the degree of irritation. The data on
the outcome of the experiment are given in the following table:
Rat
1
2
3
4 5
7
1.0
A B C| Rank A Rank B Rank C
6
5
3
11.5
6.0
1.5
9 8 4
23.0
20.0
3.0
6
11.5
23.0
1.5
6.0
20.0
11.5
16.5
20.0
23.0
6.0
16.5
11.5
11.5
16.5
6.0
11.5
6.0
16.5
5
6
7
8
Σyi
1.0
9 3
8
6
8 9
7 6
7 5
7
50 57 43
10
5
6
6 5
10
For the original data set 1-1 ij = 150, and ₁1-13 = 1006. From the
ranks of the original data set the rank sums are RA = 97.5, RB = 128, Rc = 74.5
respectively.
At a = 1%, is there sufficient evidence to support the research hypothesis that
the probability distributions of skin irritation scores for the 3 chemicals differ in
location?
(a) Stating relevant hypotheses, test the above research hypothesis by using an
appropriate nonparametric test.
(b) Stating relevant hypotheses, test the above research hypothesis by using an
appropriate parametric test.
(c) In both of the above tests, state the underlying assumptions and discuss the
differences in the assumptions for the two different tests.
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