33.
, don’t reject H
35.
, so don’t reject H
.
37. a. b.
Between and .376
39. a.
Yes
b.
, so H should be
rejected.
41. a. b.
Yes. Since , at
level .05 there would appear to be an increase, but not at level .01.
c.
7.02, 10.06
43. a.
No
b. c.
49.1
45. a.
Yes, because of the linear pattern in a normal probability plot.
b.
No, data is paired, not independent samples
c.
, same conclusion.
47. a.
; plausible that they are identical
b.
Linear pattern in npp implies normality of difference dis- tribution is plausible.
49. H
is rejected because
51.
, so H cannot be rejected.
53. a.
, so don’t reject H .
b. 55. a.
The CI for is
. Taking the antilogs of the lower and upper limits gives a CI for u itself.
b.
1.43, 2.31; aspirin appears to be beneficial.
57. 59. a.
3.69
b.
4.82
c.
.207
d.
.271
e.
4.30
f.
.212
g.
.95
h.
.94 2.35, .07
n 2 yny]
12
mx 1 lnˆu 6 z
a 2
[m 2 x lnu
n 5 1211
z 5 .80 , 1.96
P -value 5 .4247
2 4.18 22.33
95 CI: 22.52, 1.05 t 5
3.66, P-value 5 .001 not .003 2
49.1 P
-value 5 .02 23.85, 11.35
t 5 2.7, P-value 5 .018 , .05 5 a
2 1.224
2.561, 2.287 t 5 2
2.2, df 5 16, P-value 5 .021 . .01 5 a No, t 5 1.33, P-value 5 .094
61.
; since , don’t reject H
.
63.
, so reject H ; there does appear to be more
variability in low-dose weight gain.
65. 67.
No. , so reject
using either .
69.
, so cannot be
rejected.
71. 73.
They appear to differ, since .
75.
Yes, t ⫽ ⫺2.25, df ⫽ 57, P-value .028.
77. a.
No.
b.
No.
79.
, so H is rejected at level .05 or .01.
81.
No, nor should the two-sample t test be used, because a nor- mal probability plot suggests that the good-visibility distri-
bution is not normal.
83.
Unpooled: Pooled:
85. a. b.
87.
No,
89.
.9015, .8264, .0294, .0000; true average IQs; no
91.
Yes;
93. a.
Yes. , and
b.
, so don’t reject H .
95.
21.29, 2.59 t 5
1.1, P-value 5 .14 P
-value 0 t 5 2
6.4, df 5 57 z 5
4.2, P-value 0 z 5
.83, P-value .20 m 5
240, n 5 160 m 5
141, n 5 47 df 5 24, t 5 21.9, P-value .070
df 5 15, t 5 21.8, P-value .092 t 5
3.9, P-value 5 .004 t 5 2
.56, P-value .29 t 5 2
2.84, df 5 18, P-value .012 P
-value 5 0 df 5 14, t 5 25.19,
2299.3, 1517.9 H
: p
1
2 p
2
5 z .
1 P
-value . .5 a 5
.05 or .01 H
: m
1
2 m
2
5 t 5
3.2, df 5 15, P-value 5 .006 s
2 2
F
12a2
s
1 2
, s
2 2
F
a 2
s
1 2
; .023, 1.99 f 5
2.85 2.08 .167 , .384 , 3.63
f 5 .384
Chapter 10
1. a.
, so don’t reject H .
b. 3.
, so . H
cannot be rejected at any reasonable significance level.
5.
, so the three grades don’t appear to differ.
7.
, so H can be rejected at any reason-
able significance level.
9.
and , so
. Thus H can be rejected at signifi-
cance level .05; there appear to be differences among the grains.
11.
3 1
4 2
5 437.5
462.0 469.3
512.8 532.1
Brands 2 and 5 don’t appear to differ, nor does there appear to be any difference between brands 1, 3, and 4, but each
w 5 36.09
.01 , P-value , .05 F
.05, 3, 20
5 3.10 , 3.96 , 4.94 5 F
.01,3,20
f 5 3.96
f 5 51.3, P-value 5 0
f 5 1.73 , 5.49 5 F
.01, 2, 27
P -value . .10
f 5 1.30 , 2.57 5 F
.10, 2, 21
P -value . .10
f 5 1.85 , 3.06 5 F
.05, 4, 15
brand in the first group appears to differ significantly from all brands in the second group.
13.
3 1
4 2
5 427.5
462.0 469.3
502.8 532.1
15.
14.18 17.94
18.00 18.00
25.74 27.67
17. 19.
Any value of SSE between 422.16 and 431.88 will work.
21. a.
and , so reject H
.
b. 23.
1 2
3 4
1 –
2 –
– 3
– –
– 4
– –
– –
4 3
2 1
5.35 6 5.81 9.90 6 5.81
4.55 6 6.13 12.78 6 5.48
7.43 6 5.81 2.88 6 5.81
299.16, 235.64, 29.34, 94.16 F
.01, 5, 78
3.3 f 5
22.6 2.029, .379
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.
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.
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