Chapter 11
0
H
1
H
11.2
0
H
: I will complete the Ph.D.
1
H
: I will not be able to complete the Ph.D.
0
H
1
H
0
H
1
H
11.5
1
H
: The plane is on fire
1
H
: The plane is not on fire
11.6 The defendant in both cases was O. J. Simpson. The verdicts were logical because in the
All p-values and probabilities of Type II errors were calculated manually using Table 3 in
Appendix B.
11.7 Rejection region: z <
575.2
005.−=−z
or z >
005.
z
= 2.575
11.8 Rejection region: z >
03.
z
= 1.88
11.9 Rejection region: z <
28.1
10.−=−z
75.1
25/2
153.14
n/
x
z−=
−
=
−
=
11.10 Rejection region: z <
96.1
025.
−=−z
or z >
025.
z
= 1.96
There is not enough evidence to infer that
100.
11.11 Rejection region: z >
01.
z
= 2.33
11.12 Rejection region: z <
645.1
05.−=−z
b.
00.2
25/5
5052
n/
x
z=
−
=
−
=
d. The value of the test statistic increases and the p-value decreases.
11.14a.
60.
9/50
200190
n/
x
z−=
−
=
−
=
d. The value of the test statistic decreases and the p-value decreases.
11.15 a.
00.1
25/5
2021
n/
x
z=
−
=
−
=
d. The value of the test statistic increases and the p-value decreases.
11.16 a.
25.1
100/8
10099
n/
x
z−=
−
=
−
=
p-value = 2P(Z < –1.25) = 2(.1056) = .2112
11.17 a.
00.4
100/25
1000990
n/
x
z−=
−
=
−
=
p-value = P(Z < –4.00) = 0
b.
00.2
100/50
1000990
n/
x
z−=
−
=
−
=
00.1
1000990
n/
x
z−=
−
=
−
=
11.18 a.
00.3
25/20
6072
n/
x
z=
−
=
−
=
p-value = P(Z > 3.00) = 1 – .9987 = .0013
00.2
11.19 a
74.1
200/65
170178
n/
x
z=
−
=
−
=
p-valu.e = P(Z > 1.74) = 1 – .9591 = .0409
b.
23.1
100/65
170178
n/
x
z=
−
=
−
=
11.21 See Table 11.1 in the book.
11.22 a
62.
100/6
2263.21
n/
x
z−=
−
=
−
=
38.1
500/6
2263.21
n/
x
z−=
−
=
−
=
11.23 a
83.1
220/3
2263.21
n/
x
z−=
−
=
−
=
11.24
x
220/6
22x
z−
=
p-value
22.0 0 .5
21.8 –.49 .3121
11.25 a
84.
50/87.3
09.1755.17
n/
x
z=
−
=
−
=
p-value = 2P(Z > 2.38) = 2(1 – .9913) = 2(.0087) = .0174
The value of the test statistic increases and the p-value decreases.
11.27a
x
100/87.3
09.17x
z−
=
p-value
15.0 –5.40 0
15.5 –4.11 0
11.28
:H0
= 5
:H1
> 5
11.29
:H0
= 50
:H1
> 50
11.30
:H0
= 12
:H1
< 12
11.31
:H0
= 36
:H1
< 36
11.32
:H0
= 6
:H1
11.33
:H0
= .50
:H1
.50
11.34
:H0
= 25
:H1
> 25
11.35
:H0
= 5,000
:H1
> 5,000
11.36
:H0
= 30,000
:H1
< 30,000
11.37
:H0
= 560
:H1
> 560
11.38a
:H0
= 17.85
:H1
> 17.85
11.39
:H0
= 0
:H1
< 0
:H1
11.41
:H0
= 4
:H1
> 4
11.42
:H0
= 20
:H1
< 20
11.43
:H0
= 100
:H1
11.44
:H0
= 4
:H1
4
11.45
:H0
= 5
:H1
> 5
11.46
:H0
= 32
:H1
< 32
11.47
:H0
= 230
:H1
> 230
11.48 Rejection region:
n/
x
−
>
2/
z
or
n/
x
−
<
2/
z
−
11.49 Rejection region:
n
x
/
−
>
z
25/50
1000−x
>
33.2
01.=z
x
> 1023.3