25. a.
, so reject H .
b.
.1056
c.
217
27. a.
. A box- plot shows substantial positive skew; there are no outliers.
b.
No. A normal probability plot shows substantial curva- ture. No, since n is large.
c.
; reject H at any reasonable significance
level; yes.
d.
.821
29. a.
No, since
b.
.30 from software
31.
No, since
33. a.
No, since
b.
Yes, type II
c.
.66 from software
37. a.
No, since
b.
I: say that more than 20 are obese when this is not the case; II: conclude that 20 are obese when the actual
percentage exceeds 20.
c.
.121
39.
, so reject . No.
41. a. z
1.0, so there is not enough evidence to conclude that
thus, use screwtops.
b.
I: Don’t use screwtops when their use is justified; II: Use screwtops when their use isn’t justified.
43. a.
, reject H and the company’s premise.
b.
.0332
45.
No, no, yes.
47. a.
Reject H .
b.
Reject H .
c.
Don’t reject H .
d.
Reject H . a close call
e.
Don’t reject H .
49. a.
.0778
b.
.1841
c.
.0250
d.
.0066
e.
.5438
51. a.
.040
b.
.018
c.
.130
d.
.653
e. f.
.000 ,
.005 R 5
55, 6, c
, 24, 25 6, a 5 .098, b 5 .090
z 5 3.07 2.58
p , .25;
2 5
H : p 5 .40
z 5 3.67 2.58
1.28 , 1.645 2.44 , 2.539
1.04 , 2.132 1.19 , 1.796
z 5 2 5.79
x 5 .750, x| 5 .640, s 5 .3025, f
s
5 .480
z 5 2 3.33 22.58
53.
, so don’t reject H ; no apparent difference.
55.
, so should be rejected in
favor of .
57.
No, since
59. a. Yes b. The P-value slightly exceeds .10, so
should not be rejected, and the concrete should be used.
61.
, so . H
should therefore not be rejected.
63. a.
.8980, .1049, .0014
b.
. Yes.
c.
No
65.
, so H should be rejected.
67. a.
versus
b. H
cannot be rejected for either a.
69. a.
No, because ; yes, because 45.31
greatly exceeds 20, but n is very small.
b. 71. a.
No; no
b.
No, because and
.
73. a.
Approximately .6; approximately .2 from Appendix Table A.17
b. 75. a.
, so H cannot be rejected; Type II
b.
.10. Yes.
77.
Yes. , so
H should be rejected.
79.
No, since .
81.
Yes, since and
83. a.
, so do not reject H ; no contradiction
85. a.
For , reject
H if
b.
, so do not reject H .
87. a.
Yes, a 5 .002 Test statistic value 5 19.65 . 8.260
2 g
x
i
m x
12a, 2n 2
H
a
: m , m .01 , P-value , .025
P -value 5 0 , .05
z 5 4.4
z 5 1.33 , 2.05
z 5 2 3.32 23.08
z 5 1.64 , 1.96
n 5 28
P -value 5 .33 . .10
z 5 .44
b 5 .3 software
P -value 5 .02 . .01
H
a
: m 2 .85 H
: m 5 .85 z 5 2
3.12 21.96 P
-value 0 P
-value .116 t
1.9 H
: m 5 100 P
-value 5 .2266 H
a
: m 2 5 H
: m 5 5 P
-value , .0004 , .01 P
-value . a
Chapter 9
1. a.
; it doesn’t
b.
.0724, .2691
c.
No
3.
, so don’t reject H .
5. a.
, so reject H .
b.
.0019
c.
.8212
d.
66
7.
No, since P-value for a 2-tailed test is .0602.
9. a.
6.2; yes
b.
, , no
c.
No
d.
A 95 CI is 10.0, 21.8.
11.
A 95 CI is .99, 2.41.
13.
50
15. b.
It increases.
17. a.
17
b.
21
c.
18
d.
26
19.
, so do not reject H .
t 5 2 1.20 . 2t
.01,9
5 2 2.821
P -value .25
z 5 1.14
z 5 2 2.90
z 5 1.76 , 21.33
2 .4 hr
21.
Yes; , so reject H
.
23. b.
No
c.
for any reasonable a, so don’t reject
.
25.
.3, 6.1, yes, yes
27. a.
99 CI: .33, .71
b.
99 CI: , so 0 is a
plausible value of the difference.
29.
. At significance level .05, we would conclude that cola results in a higher average
strength, but not at significance level .01.
31. a.
Virtually identical centers, substantially more variability in medium range observations than in higher range obser-
vations
b.
, based on 23 df; no 27.9, 9.6
t 5 2 2.10, df 5 25, P-value 5 .023
2.07, .41 H
P-value .7 t 5 2
.38 . 2t
a 2, 10
2 2.64 22.602
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33.
, don’t reject H
35.
, so don’t reject H
.
37. a. b.