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Chapter 12 - Chapter 12 12.1 a x t 2 s n = 510 2.064(125 25...

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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 = 65.71 251
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d 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 - = p-value = .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 - = p-value = .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 - = p-value = .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 p-value 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 - = p-value = .0015. There is enough evidence to infer that the population mean is not equal to 180. b , 57 . 1 200 / 45 180 175 n / s x t - = - = μ - = p-value = .1177. There is not enough evidence to infer that the population mean is not equal to 180. c , 18 . 1 200 / 60 180 175 n / s x t - = - = μ - = p-value = .2400. There is not enough evidence to infer that the population mean is not equal to 180. d. As the s increases, the test statistic increases and the p-value increases. 12.9 Rejection region: 660 . 1 t t t 99 , 05 . 1 n , - - = - < - α 252
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a , 00 . 1 100 / 50 150 145 n / s x t - = - = μ - = p-value = .1599. There is not enough evidence to infer that the population mean is less than 150. b , 00 . 2 100 / 50 150 140 n / s x t - = - = μ - = p-value = .0241. There is enough evidence to infer that the population mean is less than 150. c , 00 . 3 100 / 50 150 135 n / s x t - = - = μ - = p-value = .0017. There is enough evidence to infer that the population mean is less than 150 d The test statistics decreases and the p-value decreases. 12.10 μ : H 0 = 50 μ : H 0 50 a Rejection region: 711 . 1 t t t 24 , 05 . 1 n , 2 / - = - = - < - α or 711 . 1 t t t 24 , 05 . 1 n , 2 / = = - α , 67 . 25 / 15 50 52 n / s x t = - = μ - = p-value = .5113. There is not enough evidence to infer that the population mean is not equal to 50.
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