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A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Question 8
A product developer is investigating the tensile strength of a new synthetic fiber that will be used to make
cloth for men's shirts. Strength is usually affected by the percentage of cotton used in the blend of
materials for the fiber. The engineer conducts a completely randomized experiment with five levels of
cotton content and replicates the experiment five times. The data are shown in the following table.
Cotton strength
Cotton weight Rep
percentage
15
15
15
15
15
20
20
20
20
20
25
25
25
25
25
30
30
30
30
30
35
35
این این این
35
35
35
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
7
7
15
11
9
12
17
12
18
18
14
19
19
18
18
19
25
22
19
23
7
10
11
15
11
(a) Construct the appropriate experimental design to get the above cotton strength
(b) Is there evidence to support the claim that cotton content affects the mean tensile strength? Use
α = 0.05.
(c) Analyze the residuals from this experiment and comment on model adequacy.
(d) Predict probability of getting predicted cotton strength relying on different cotton weight.
Transcribed Image Text:Question 8 A product developer is investigating the tensile strength of a new synthetic fiber that will be used to make cloth for men's shirts. Strength is usually affected by the percentage of cotton used in the blend of materials for the fiber. The engineer conducts a completely randomized experiment with five levels of cotton content and replicates the experiment five times. The data are shown in the following table. Cotton strength Cotton weight Rep percentage 15 15 15 15 15 20 20 20 20 20 25 25 25 25 25 30 30 30 30 30 35 35 این این این 35 35 35 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 1 2 3 4 5 7 7 15 11 9 12 17 12 18 18 14 19 19 18 18 19 25 22 19 23 7 10 11 15 11 (a) Construct the appropriate experimental design to get the above cotton strength (b) Is there evidence to support the claim that cotton content affects the mean tensile strength? Use α = 0.05. (c) Analyze the residuals from this experiment and comment on model adequacy. (d) Predict probability of getting predicted cotton strength relying on different cotton weight.
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