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
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