1. a.
, so don’t reject H
0A
.
b.
, so don’t reject H
0B
.
3. a.
, so conclude that there is a gas rate effect;
, so conclude that there is a liquid rate effect.
b.
, so only the lowest two rates do not differ significantly from one another.
c.
336.75 382.25 419.25 473 so only the lowest and highest rates appear to differ significantly from one another.
5.
, so there appears to be no effect due to angle of pull.
7. a. Source df
SS MS
f
Treatments 2
28.78 14.39
1.04 Blocks
17 2977.67
175.16 12.68
Error 34
469.55 13.81
Total 53
3476.00 True average adaptation score does not appear to depend on
which treatment is given. b. Yes; f
B
is quite large, suggest- ing great variability between subjects.
9. Source df
SS MS
f F
.05
Treatments 3
81.19 27.06
22.4 3.01
Blocks 8
66.50 8.31
Error 24
29.06 1.21
Total 35
176.75
11.
A normal probability plot of the residuals shows a substan- tial linear pattern. There is no discernible pattern in a plot
of the residuals versus the fitted values.
13. b.
Each SS is multiplied by c
2
, but f
A
and f
B
are unchanged.
15. a.
Approximately .20, .43
b.
Approximately .30
17. a.
, and , so
the amount of carbon fiber addition appears significant.
b. f
A
5 6.54, f
B
5 5.33, f
AB
5 .27
F
.05,2,9
5 4.26
f
A
5 3.76, f
B
5 6.82, f
AB
5 .74
8.56 9.22 10.78 12.44 2
3 4
1 f
A
5 2.56,
F
.01,3,12
5 5.95
w 5 95.44; 231.75 325.25 441.0 613.25
f
B
5 13.0
f
A
5 105.3 F
.01,3.9
f
B
5 2.98
f
A
5 1.55
25. a.
Normal, equal variances
b.
, H should not be
rejected
27. a.
, so brands appear to differ.
b.
Normality is quite plausible a normal probability plot of the residuals
shows a linear pattern.
c.
4 3 2 1 Only brands 1 and 4 appear to differ significantly.
31.
Approximately .62
33. 35. a.
, so H is not rejected.
b.
, so again H is not rejected.
.029 . .01 3.68 , 4.94
arcsin 1xn x
ij
2 x
i
f 5 3.75 3.10 5 F
.05, 3, 20
P-value . .10 SSTr 5 8.33, SSE 5 77.79, f 5 1.7
Chapter 11
19. a. Source df
SS MS
f
Coal 2
1.00241 .50121
29.49 NaOH
2 .12431
.06216 3.66
Interaction 4
.01456 .00364
.21 Error
9 .15295
.01699 Total
17 1.29423
Type of coal does appear to affect total acidity.
b.
Coals 1 and 3 don’t differ significantly from one another, but both differ significantly from coal 2.
21. a, b. Source df
SS MS
f
A 2
22,941.80 11,470.90
22.98 B
4 22,765.53
5691.38 5.60
AB 8
3993.87 499.23
.49 Error
15 15,253.50
1016.90 Total
29 64,954.70
H
0A
and H
0B
are both rejected.
23. Source df
SS MS
f
A 2
11,573.38 5786.69
B 4
17,930.09 4482.52
AB 8
1734.17 216.77
Error 30
4716.67 157.22
Total 44
35,954.31 Since ,
and ,
H
0G
is not rejected but both H
0A
and H
0B
are rejected.
25. 27. a. Source df
SS MS
f F
.05
A 2
14,144.44 7072.22
61.06 3.35
B 2
5511.27 2755.64
23.79 3.35
C 2 244,696.39 122,348.20 1056.27
3.35 2.373, 2.033
F
.01,4,30
5 4.02
F
.01,8,30
5 3.17, F
.01,2,8
5 8.65
MSAB MSE
5 1.38 MSB
MSE 5 28.51
MSA MSAB
5 26.70
37.
, so and H
should be rejected.
5 3 1 4 2 This underscoring pattern is a bit awkward to interpret.
39.
The CI is , which does include 0.
41.
, so cannot be rejected.
43.
Only among these four contrasts appears to differ
significantly from zero.
45.
They are identical. m
1
2 m
3
23.70, 1.04, 24.83, 2.33, 23.77, 1.27, 23.99, .15. H
: s
A 2
5 f 5
3.96 , 4.07 2.144, .474
P -value , .001
f 5 8.44 . 6.49 5 F
.001
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook andor eChapters. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
AB 4
1069.62 267.41
2.31 2.73
AC 4
62.67 15.67
.14 2.73
BC 4
331.67 82.92
.72 2.73
ABC 8
1080.77 135.10
1.17 2.31
Error 27 3127.50
115.83 Total 53 270,024.33
d.
, and all three of the levels dif- fer significantly from one another.
29. a. Source df
SS MS
f
A 2
12.896 6.448
1.04 B
1 100.041
100.041 16.10
C 3
393.416 131.139
21.10 AB
2 1.646
.823 AC
6 71.021
11.837 1.905
BC 3
1.542 .514
ABC 6
9.771 1.629
Error 72
447.500 6.215
Total 95
1037.833
b.
No interaction effects are significant.
c.
Factor B and factor C main effects are significant.
d.
; only machines 2 and 4 do not differ signifi- cantly from one another.
31.
The P-value column shows that several interaction effects are significant at level .01.
33. Source df
SS MS
f
A 6
67.32 11.02
B 6
51.06 8.51
C 6
5.43 .91
.61 Error
30 44.26
1.48 Total
48 168.07
, so H
0C
is not rejected.
35.
Source df
SS MS
f
A 4
28.88 7.22
10.7 B
4 23.70
5.93 8.79
C 4
.62 .155
Error 12
8.10 .675
Total 24
61.30 Since ,
both A
and B are significant.
37.
Source df
MS f
A 2
2207.329 2259
B 1
47.255 48.4
C 2
491.783 503
D 1
.044 AB
2 15.303
15.7 AC
4 275.446
282 AD
2 .470
BC 2
2.141 2.19
BD 1
.273 CD
2 .247
ABC 4
3.714 3.80
, 1
, 1
, 1
, 1
F
.05,4,12
5 3.26
, 1
F
.05,6,30
5 2.42,
f
C
5 .61
w 5 1.89
, 1
, 1
, 1
Q
.05,3,27
5 3.51,
w 5 8.90
ABD 2
4.072 4.17
ACD 4
.767 BCD
2 .280
ABCD 4
.347 Error
36 .977
Total 71
93.621 Denotes a significant F ratio.
39. a.
.
b. Effect
Source Contrast
MS f
A 1307
71,177.04 436.7
B 1305
70,959.34 435.4
C 529
11,660.04 71.54
AB 199
1650.04 10.12
AC ⫺
53 117.04
BC 57
135.38 ABC
27 30.38
Error 162.98
41. Source SS
f
A 136,640.02
1007.6 B
139,644.19 1029.8
C 24,616.02
181.5 D
20,377.52 150.3
AB 2173.52
16.0 AC
2.52 AD
58.52 BC
165.02 1.2
BD 9.19
CD 17.52
ABC 42.19
ABD 117.19
ACD 188.02
1.4 BCD
13.02 ABCD
204.19 1.5
Error 4339.33
Total 328,607.98
, so only the four main effects and the AB interaction appear significant.
43. Source df
SS f
A 1
.436 B
1 .099
C 1
.109 D
1 414.12
851 AB
1 .003
AC 1
.078 AD
1 .017
BC 1
1.404 3.62
BD 1
.456 CD
1 2.190
4.50 Error
5 2.434
, so only the factor D main effect is judged significant.
F
.05,1,5
5 6.61
, 1
, 1
, 1
, 1
, 1
, 1
, 1
F
.05,1.32
4.15 ,
1 ,
1 ,
1 ,
1 ,
1 ,
1 ,
1 ,
1 ,
1 ,
1 bˆ
1
5 54.38, gˆ
11 AC
5 2 2.21, gˆ
21 AC
5 2.21
, 1
, 1
, 1
Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook andor eChapters. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it.
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