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.
45. a.
1: 1, ab, cd, abcd; 2: a, b, acd, bcd; 3: c, d, abc, abd; 4: ac, bc, ad, bd.
b. Source
df SS
f
A 1
12,403.125 27.18
B 1
92,235.125 202.13
C 1
3.125 0.01
D 1
60.500 0.13
AC 1
10.125 0.02
AD 1
91.125 0.20
BC 1
50.000 0.11
BD 1
420.500 0.92
ABC 1
3.125 0.01
ABD 1
0.500 0.00
ACD 1
200.000 0.44
BCD 1
2.000 0.00
Blocks 7
898.875 0.28
Error 12
5475.750 Total
31 111,853.875
, so only the A and B main effects are sig- nificant.
47. a. ABFG;
1, ab, cd, ce, de, fg, acf, adf, adg, aef, acg, aeg, bcg, bcf, bdf, bdg, bef, beg, abcd, abce, abde, abfg, cdfg,
cefg, defg, acdef, acdeg, bcdef, bcdeg, abcdfg, abcefg, abdefg.
{A, BCDE, ACDEFG, BFG}, {B, ACDE, BCDEFG, AFG
}, {C, ABDE, DEFG, ABCFG}, {D, ABCE, CEFG, ABDFG
}, {E, ABCD, CDFG, ABEFG}, {F, ABCDEF, CDEG, ABG}, {G, ABCDEG, CDEF, ABF}
. b. 1: 1, aef, beg, abcd, abfg, cdfg, acdeg, bcdef; 2: ab, cd, fg, aeg, bef, acdef, bcdeg, abcdfg;
3: de, acg, adf, bcf, bdg, abce, cefg, abdefg;
4: ce, acf, adg, bcg, bdf, abde, defg, abcefg.
49.
SSA 2.250, SSB 7.840, SSC .360, SSD 52.563, SSE 10.240, SSAB 1.563, SSAC 7.563, SSAD
.090, SSAE 4.203, SSBC 2.103, SSBD .010, SSBE .123, SSCD .010, SSCE .063, SSDE
4.840. Error SS sum of two-factor SS’s 20.568, Error MS 2.057,
10.04, so only the D main effect is significant.
51. Source df
SS MS
f
A main effects
1 322.667
322.667 980.38
B main effects
3 35.623
11.874 36.08
Interaction 3
8.557 2.852
8.67 Error
16 5.266
0.329 Total
23 372.113
, so interactions appear to be present. F
.05,3.16
5 3.24
F
.01,1,10
5 F
.01,1,12
5 9.33
53. Source df
SS MS
f
A 1
30.25 30.25
6.72 B
1 144.00
144.00 32.00
C 1
12.25 12.25
2.72 AB
1 1122.25
1122.25 249.39
AC 1
1.00 1.00
.22 BC
1 12.25
12.25 2.72
ABC 1
16.00 16.00
3.56 Error
4 36.00
4.50 Total
7 Only the main effect for B and the AB interaction effect
are significant at .
55. a.
b.
A normal probability plot suggests that the A, C, and D main effects are quite important, and perhaps the CD
interaction. In fact, pooling the 4 three-factor interaction SS’s and the four-factor interaction SS to obtain an SSE
based on 5 df and then constructing an ANOVA table suggests that these are the most important effects.
57. Source df
SS MS
f F
.01
A 2
67,553 33,777
11.37 5.49
B 2
72,361 36,181
12.18 5.49
C 2
442,111 221,056
74.43 5.49
AB 4
9696 2424
0.82 4.11
AC 4
6213 1553
0.52 4.11
BC 4
34,928 8732
2.94 4.11
ABC 8
33,487 4186
1.41 3.26
Error 27
80,192 2970
Total 53
746,542 All main effects are significant, but there are no significant
interactions.
59.
Based on the P-values in the ANOVA table, statistically sig- nificant factors at the level
are adhesive type and cure time. The conductor material does not have a statisti-
cally significant effect on bond strength. There are no sig- nificant interactions.
61. Source df
SS MS
f
A 4
285.76 71.44
.594 B
4 227.76
56.94 .473
C 4
2867.76 716.94
5.958 D
4 5536.56
1384.14 11.502
Error 8
962.72 120.34
F
.05,4.8
3.84 Total
24 H
0A
and H
0B
cannot be rejected, while H
0C
and H
0D
are rejected.
a 5 .01
bˆg
11
5 .50, dˆg
11
5 4.50
.75, bˆd
11
5 aˆb
11
5 0, aˆd
11
5 2.00, aˆg
11
5 2.75,
gˆ
1
5 21.00,
dˆ
1
5 17.00,
b ˆ
1
5 2.25,
a ˆ
1
5 9.00,
a 5 .01
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.
