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
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