Solucionario Walpole 8 ED
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Solucionario Walpole 8 ED

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has
changed as follows.
Source of Sum of Degrees of Mean Computed
Variation Squares Freedom Square f
Paint Types
Error
2.6308
3.2516
2
15
1.3154
0.2168
6.07
Total 5.8824 17
with P -value= 0.0117.
Decision: Reject H0 at level 0.05; the average wearing quality differ significantly
for three paints. The residual and normal probability plots are shown here:
1.0 1.5 2.0 2.5 3.0
\u2212
0.
8
\u2212
0.
6
\u2212
0.
4
\u2212
0.
2
0.
0
0.
2
0.
4
0.
6
Type
R
es
id
ua
l
\u22122 \u22121 0 1 2
\u2212
0.
8
\u2212
0.
6
\u2212
0.
4
\u2212
0.
2
0.
0
0.
2
0.
4
0.
6
Theoretical Quantiles
Sa
m
pl
e 
Qu
an
tile
s
While the homogeneity of the variances seem to be a little better, the normality
assumption may still be invalid.
212 Chapter 13 One-Factor Experiments: General
13.67 (a) The hypotheses are
H0 : \u3b11 = \u3b12 = \u3b13 = \u3b14 = 0,
H1 : At least one of the \u3b1i\u2019s is not zero.
Computation:
Source of Sum of Degrees of Mean Computed
Variation Squares Freedom Square f
Locations
Error
0.01594
0.00616
3
16
0.00531
0.00039
13.80
Total 0.02210 19
with P -value= 0.0001.
Decision: Reject H0; the mean ozone levels differ significantly across the locations.
(b) Using Tukey\u2019s test, the results are as follows.
y¯4. y¯1. y¯3. y¯2.
0.078 0.092 0.096 0.152
Location 2 appears to have much higher ozone measurements than other locations.
Chapter 14
Factorial Experiments (Two or More
Factors)
14.1 The hypotheses of the three parts are,
(a) for the main effects temperature,
H
\u2032
0 : \u3b11 = \u3b12 = \u3b13 = 0,
H
\u2032
1 : At least one of the \u3b1i\u2019s is not zero;
(b) for the main effects ovens,
H
\u2032\u2032
0 : \u3b21 = \u3b22 = \u3b23 = \u3b24 = 0,
H
\u2032\u2032
1 : At least one of the \u3b2i\u2019s is not zero;
(c) and for the interactions,
H
\u2032\u2032\u2032
0 : (\u3b1\u3b2)11 = (\u3b1\u3b2)12 = · · · = (\u3b1\u3b2)34 = 0,
H
\u2032\u2032\u2032
1 : At least one of the (\u3b1\u3b2)ij\u2019s is not zero.
\u3b1 = 0.05.
Critical regions: (a) f1 > 3.00; (b) f2 > 3.89; and (c) f3 > 3.49.
Computations: From the computer printout we have
Source of Sum of Degrees of Mean Computed
Variation Squares Freedom Square f
Temperatures
Ovens
Interaction
Error
5194.08
4963.12
3126.26
3833.50
2
3
6
12
2597.0400
1654.3733
521.0433
319.4583
8.13
5.18
1.63
Total 17, 116.96 23
213
214 Chapter 14 Factorial Experiments (Two or More Factors)
Decision: (a) Reject H
\u2032
0; (b) Reject H
\u2032\u2032
0 ; (c) Do not reject H
\u2032\u2032\u2032
0 .
14.2 The hypotheses of the three parts are,
(a) for the main effects brands,
H
\u2032
0 : \u3b11 = \u3b12 = \u3b13 = 0,
H
\u2032
1 : At least one of the \u3b1i\u2019s is not zero;
(b) for the main effects times,
H
\u2032\u2032
0 : \u3b21 = \u3b22 = \u3b23 = 0,
H
\u2032\u2032
1 : At least one of the \u3b2i\u2019s is not zero;
(c) and for the interactions,
H
\u2032\u2032\u2032
0 : (\u3b1\u3b2)11 = (\u3b1\u3b2)12 = · · · = (\u3b1\u3b2)33 = 0,
H
\u2032\u2032\u2032
1 : At least one of the (\u3b1\u3b2)ij\u2019s is not zero.
\u3b1 = 0.05.
Critical regions: (a) f1 > 3.35; (b) f2 > 3.35; and (c) f3 > 2.73.
Computations: From the computer printout we have
Source of Sum of Degrees of Mean Computed
Variation Squares Freedom Square f
Brands
Times
Interaction
Error
32.7517
227.2117
17.3217
254.7025
2
2
4
27
16.3758
113.6058
4.3304
9.4334
1.74
12.04
0.46
Total 531.9875 35
Decision: (a) Do not reject H
\u2032
0; (b) Reject H
\u2032\u2032
0 ; (c) Do not reject H
\u2032\u2032\u2032
0 .
14.3 The hypotheses of the three parts are,
(a) for the main effects environments,
H
\u2032
0 : \u3b11 = \u3b12 = 0, (no differences in the environment)
H
\u2032
1 : At least one of the \u3b1i\u2019s is not zero;
(b) for the main effects strains,
H
\u2032\u2032
0 : \u3b21 = \u3b22 = \u3b23 = 0, (no differences in the strains)
H
\u2032\u2032
1 : At least one of the \u3b2i\u2019s is not zero;
Solutions for Exercises in Chapter 14 215
(c) and for the interactions,
H
\u2032\u2032\u2032
0 : (\u3b1\u3b2)11 = (\u3b1\u3b2)12 = · · · = (\u3b1\u3b2)23 = 0, (environments and strains do not interact)
H
\u2032\u2032\u2032
1 : At least one of the (\u3b1\u3b2)ij\u2019s is not zero.
\u3b1 = 0.01.
Critical regions: (a) f1 > 7.29; (b) f2 > 5.16; and (c) f3 > 5.16.
Computations: From the computer printout we have
Source of Sum of Degrees of Mean Computed
Variation Squares Freedom Square f
Environments
Strains
Interaction
Error
14, 875.521
18, 154.167
1, 235.167
42, 192.625
1
2
2
42
14, 875.521
9, 077.083
617.583
1004.586
14.81
9.04
0.61
Total 76, 457.479 47
Decision: (a) Reject H
\u2032
0; (b) Reject H
\u2032\u2032
0 ; (c) Do not reject H
\u2032\u2032\u2032
0 . Interaction is not
significant, while both main effects, environment and strain, are all significant.
14.4 (a) The hypotheses of the three parts are,
H
\u2032
0 : \u3b11 = \u3b12 = \u3b13 = 0
H
\u2032
1 : At least one of the \u3b1i\u2019s is not zero;
H
\u2032\u2032
0 : \u3b21 = \u3b22 = \u3b23 = 0,
H
\u2032\u2032
1 : At least one of the \u3b2i\u2019s is not zero;
H
\u2032\u2032\u2032
0 : (\u3b1\u3b2)11 = (\u3b1\u3b2)12 = · · · = (\u3b1\u3b2)33 = 0,
H
\u2032\u2032\u2032
1 : At least one of the (\u3b1\u3b2)ij\u2019s is not zero.
\u3b1 = 0.01.
Critical regions: for H
\u2032
0, f1 > 3.21; for H
\u2032\u2032
0 , f2 > 3.21; and for H
\u2032\u2032\u2032
0 , f3 > 2.59.
Computations: From the computer printout we have
Source of Sum of Degrees of Mean Computed
Variation Squares Freedom Square f
Coating
Humidity
Interaction
Error
1, 535, 021.37
1, 020, 639.15
1, 089, 989.63
5, 028, 396.67
2
2
4
45
767, 510.69
510, 319.57
272, 497.41
111, 742.15
6.87
4.57
2.44
Total 76, 457.479 47
Decision: Reject H
\u2032
0; Reject H
\u2032\u2032
0 ; Do not reject H
\u2032\u2032\u2032
0 . Coating and humidity do not
interact, while both main effects are all significant.
216 Chapter 14 Factorial Experiments (Two or More Factors)
(b) The three means for the humidity are y¯L = 733.78, y¯M = 406.39 and y¯H = 638.39.
Using Duncan\u2019s test, the means can be grouped as
y¯M y¯L y¯H
406.39 638.39 733.78
Therefore, corrosion damage is different for medium humidity than for low or high
humidity.
14.5 The hypotheses of the three parts are,
(a) for the main effects subjects,
H
\u2032
0 : \u3b11 = \u3b12 = \u3b13 = 0,
H
\u2032
1 : At least one of the \u3b1i\u2019s is not zero;
(b) for the main effects muscles,
H
\u2032\u2032
0 : \u3b21 = \u3b22 = \u3b23 = \u3b24 = \u3b25 = 0,
H
\u2032\u2032
1 : At least one of the \u3b2i\u2019s is not zero;
(c) and for the interactions,
H
\u2032\u2032\u2032
0 : (\u3b1\u3b2)11 = (\u3b1\u3b2)12 = · · · = (\u3b1\u3b2)35 = 0,
H
\u2032\u2032\u2032
1 : At least one of the (\u3b1\u3b2)ij\u2019s is not zero.
\u3b1 = 0.01.
Critical regions: (a) f1 > 5.39; (b) f2 > 4.02; and (c) f3 > 3.17.
Computations: From the computer printout we have
Source of Sum of Degrees of Mean Computed
Variation Squares Freedom Square f
Subjects
Muscles
Interaction
Error
4, 814.74
7, 543.87
11, 362.20
2, 099.17
2
4
8
30
2, 407.37
1, 885.97
1, 420.28
69.97
34.40
26.95
20.30
Total 25, 819.98 44
Decision: (a) Reject H
\u2032
0; (b) Reject H
\u2032\u2032
0 ; (c) Reject H
\u2032\u2032\u2032
0 .
14.6 The ANOVA table is shown as
Source of Sum of Degrees of Mean Computed
Variation Squares Freedom Square f P -value
Additive
Temperature
Interaction
Error
1.7578
0.8059
1.7934
1.8925
1
3
3
24
1.7578
0.2686
0.5978
0.0789
22.29
3.41
7.58
< 0.0001
0.0338
0.0010
Total 6.2497 32
Solutions for Exercises in Chapter 14 217
Decision: All main effects and interaction are significant.
An interaction plot is given here.
1
1
3.
0
3.
2
3.
4
3.
6
3.
8
4.
0
Additive
Ad
he
siv
en
es
s
2
2
3
3
4
4
0 1
 Temperature
1
2
3
4
50
60
70
80
14.7 The ANOVA table is
Source of Sum of Degrees of Mean Computed
Variation Squares Freedom Square f P -value
Temperature
Catalyst
Interaction
Error
430.475
2, 466.650
326.150
264.500
3
4
12
20
143.492
616.663
27.179
13.225
10.85
46.63
2.06
0.0003
< 0.0001
0.0745
Total 3, 487.775 39
Decision: All main effects are significant and the interaction is significant at level
0.0745. Hence, if 0.05 significance level