Statistics-Keller-Chapter 12 Solutions
Chapter 12
12.4 a x t
/ 2s /
n = 1,500
1.984(300/ 100 ) = 1,500
59.52; LCL = 1,440.48,
UCL = 1,559.52 b x t
/ 2s /
n = 1,500
1.984(200/ 100 ) = 1,500
39.68; LCL = 1,460.32,
UCL = 1,539.68 c x t
/ 2s /
n = 1,500
1.984(100/ 100 ) = 1,500
19.84; LCL = 1,480.16,
UCL = 1,519.84 d. The interval narrows.
12.6 a x t b x t c x t
/ 2s / / 2s /
/ 2s /
n = 10
1.984(1/ 100 ) = 10
.20; LCL = 9.80, UCL = 10.20
n = 10 n = 10
1.984(4/ 100 ) = 10 1.984(10/ 100 ) = 10
.79; LCL = 9.21, UCL = 10.79 1.98; LCL = 8.02, UCL = 11.98
d The interval widens.
12.8 a x t b x t c x t
/ 2s / / 2s /
/ 2s /
n = 63
1.990(8/ 81 ) = 63
1.77; LCL = 61.23, UCL = 64.77
n = 63 n = 63
2.000(8/ 64 ) = 63 2.030(8/ 36 ) = 63
2.00; LCL = 61.00, UCL = 65.00 2.71; LCL = 60.29, UCL = 65.71
d The interval widens.
12.10
H0 :
= 180 180
H1 :
Rejection region: t at x s/ n
t
/ 2,n 1
t .025,199
1.972 or t
t
/ 2,n 1
t .025,199 = 1.972
175 180 22 / 200
3.21, p-value = .0015. There is enough evidence to infer that the
population mean is not equal to 180. b t x s/ n 175 180 45 / 200 1.57, p-value = .1177. There is not enough evidence to infer that the
population mean is not equal to 180. c t x s/ n 175 180 60 / 200 1.18, p-value = .2400. There is not enough evidence to infer that the
population mean is not equal to 180.
269
d. As the s increases, the test statistic increases and the p-value increases.
12.12
H0 : H0 :
= 50 50
a Rejection region: t t x s/ n 52 50 15 / 25
t
/ 2,n 1
t .05,24
1.711 or t
t
/ 2,n 1
t .05,24
1.711
.67, p-value = .5113. There is not enough evidence to infer that the
population mean is not equal to 50. b Rejection region: t t x s/ n 52 50 15 / 15
t
/ 2,n 1
t .05,14
1.761 or t
t
/ 2,n 1
t .05,14
1.761
.52, p-value = .6136. There is not enough evidence to infer that the
12.4 a x t
/ 2s /
n = 1,500
1.984(300/ 100 ) = 1,500
59.52; LCL = 1,440.48,
UCL = 1,559.52 b x t
/ 2s /
n = 1,500
1.984(200/ 100 ) = 1,500
39.68; LCL = 1,460.32,
UCL = 1,539.68 c x t
/ 2s /
n = 1,500
1.984(100/ 100 ) = 1,500
19.84; LCL = 1,480.16,
UCL = 1,519.84 d. The interval narrows.
12.6 a x t b x t c x t
/ 2s / / 2s /
/ 2s /
n = 10
1.984(1/ 100 ) = 10
.20; LCL = 9.80, UCL = 10.20
n = 10 n = 10
1.984(4/ 100 ) = 10 1.984(10/ 100 ) = 10
.79; LCL = 9.21, UCL = 10.79 1.98; LCL = 8.02, UCL = 11.98
d The interval widens.
12.8 a x t b x t c x t
/ 2s / / 2s /
/ 2s /
n = 63
1.990(8/ 81 ) = 63
1.77; LCL = 61.23, UCL = 64.77
n = 63 n = 63
2.000(8/ 64 ) = 63 2.030(8/ 36 ) = 63
2.00; LCL = 61.00, UCL = 65.00 2.71; LCL = 60.29, UCL = 65.71
d The interval widens.
12.10
H0 :
= 180 180
H1 :
Rejection region: t at x s/ n
t
/ 2,n 1
t .025,199
1.972 or t
t
/ 2,n 1
t .025,199 = 1.972
175 180 22 / 200
3.21, p-value = .0015. There is enough evidence to infer that the
population mean is not equal to 180. b t x s/ n 175 180 45 / 200 1.57, p-value = .1177. There is not enough evidence to infer that the
population mean is not equal to 180. c t x s/ n 175 180 60 / 200 1.18, p-value = .2400. There is not enough evidence to infer that the
population mean is not equal to 180.
269
d. As the s increases, the test statistic increases and the p-value increases.
12.12
H0 : H0 :
= 50 50
a Rejection region: t t x s/ n 52 50 15 / 25
t
/ 2,n 1
t .05,24
1.711 or t
t
/ 2,n 1
t .05,24
1.711
.67, p-value = .5113. There is not enough evidence to infer that the
population mean is not equal to 50. b Rejection region: t t x s/ n 52 50 15 / 15
t
/ 2,n 1
t .05,14
1.761 or t
t
/ 2,n 1
t .05,14
1.761
.52, p-value = .6136. There is not enough evidence to infer that the