Chapter 12
12.1 a
n
/
s
t
x
2
/
α
±
= 510
±
2.064(125/
25
) = 510
±
51.60; LCL = 458.40, UCL = 561.60
b
n
/
s
t
x
2
/
α
±
= 510
±
2.009(125/
50
) = 510
±
35.51; LCL = 474.49, UCL = 545.51
c
n
/
s
t
x
2
/
α
±
= 510
±
1.984(125/
100
) = 510
±
24.80; LCL = 485.20, UCL = 534.80
d. The interval narrows.
12.2 a
n
/
s
t
x
2
/
α
±
= 1,500
±
1.984(300/
100
) = 1,500
±
59.52; LCL = 1,440.48, UCL = 1,559.52
b
n
/
s
t
x
2
/
α
±
= 1,500
±
1.984(200/
100
) = 1,500
±
39.68; LCL = 1,460.32, UCL = 1,539.68
c
n
/
s
t
x
2
/
α
±
= 1,500
±
1.984(100/
100
) = 1,500
±
19.84; LCL = 1,480.16, UCL = 1,519.84
d. The interval narrows.
12.3 a
n
/
s
t
x
2
/
α
±
= 700
±
1.645(100/
400
) = 700
±
8.23; LCL = 691.77, UCL = 708.23
b
n
/
s
t
x
2
/
α
±
= 700
±
1.96(100/
400
) = 700
±
9.80; LCL = 690.20, UCL = 709.80
a
n
/
s
t
x
2
/
α
±
= 700
±
2.576(100/
400
) = 700
±
12.88; LCL = 687.12, UCL = 712.88
d. The interval widens.
12.4 a
n
/
s
t
x
2
/
α
±
= 10
±
1.984(1/
100
) = 10
±
.20; LCL = 9.80, UCL = 10.20
b
n
/
s
t
x
2
/
α
±
= 10
±
1.984(4/
100
) = 10
±
.79; LCL = 9.21, UCL = 10.79
c
n
/
s
t
x
2
/
α
±
= 10
±
1.984(10/
100
) = 10
±
1.98; LCL = 8.02, UCL = 11.98
d The interval widens.
12.5 a
n
/
s
t
x
2
/
α
±
= 120
±
2.009(15/
51
) = 120
±
4.22; LCL = 115.78, UCL = 124.22
b
n
/
s
t
x
2
/
α
±
= 120
±
1.676(15/
51
) = 120
±
3.52; LCL = 116.48, UCL = 123.52
c
n
/
s
t
x
2
/
α
±
= 120
±
1.299(15/
51
) = 120
±
2.73; LCL = 117.27, UCL = 122.73
d The interval narrows.
12.6 a
n
/
s
t
x
2
/
α
±
= 63
±
1.990(8/
81
) = 63
±
1.77; LCL = 61.23, UCL = 64.77
b
n
/
s
t
x
2
/
α
±
= 63
±
2.000(8/
64
) = 63
±
2.00; LCL = 61.00, UCL = 65.00
c
n
/
s
t
x
2
/
α
±
= 63
±
2.030(8/
36
) = 63
±
2.71; LCL = 60.29, UCL = 65.71
237
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View Full Documentd The interval widens.
12.7
μ
:
H
0
= 20
μ
:
H
1
> 20
a Rejection region:
9
,
05
.
1
n
,
t
t
t
=

α
= 1.833
,
05
.
1
10
/
9
20
23
n
/
s
x
t
=

=
μ

=
pvalue = .1597. There is not enough evidence to infer that the population
mean is greater than 20.
b Rejection region:
29
,
05
.
1
n
,
t
t
t
=

α
= 1.699
,
83
.
1
30
/
9
20
23
n
/
s
x
t
=

=
μ

=
pvalue = .0391. There is enough evidence to infer that the population mean is
greater than 20.
c Rejection region:
≈
=

α
49
,
05
.
1
n
,
t
t
t
1.676
,
36
.
2
50
/
9
20
23
n
/
s
x
t
=

=
μ

=
pvalue = .0112. There is enough evidence to infer that the population mean is
greater than 20.
d As the sample size increases the test statistic increases [and the pvalue decreases].
12.8
μ
:
H
0
= 180
μ
:
H
1
≠
180
Rejection region:
972
.
1
t
t
t
199
,
025
.
1
n
,
2
/

≈

=

<

α
or
199
,
025
.
1
n
,
2
/
t
t
t
=

α
= 1.972
a
,
21
.
3
200
/
22
180
175
n
/
s
x
t

=

=
μ

=
pvalue = .0015. There is enough evidence to infer that the population
mean is not equal to 180.
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 Spring '08
 Schaffzin,Richard
 Normal Distribution, Standard Deviation, UCL, LCL

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