Chapter 12

# Chapter 12 - 187 Chapter 12 12.1 n s t x 2 a = 510...

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187 Chapter 12 12.1 n s t x / 2 / a ± = 510 ± 2.009(125/ 50 ) = 510 ± 35.51; LCL = 474.49, UCL = 545.51 12.2 n s t x / 2 / a ± = 510 ± 1.984(125/ 100 ) = 510 ± 24.80; LCL = 485.20, UCL = 534.80 12.3 n s t x / 2 / a ± = 510 ± 2.064(125/ 25 ) = 510 ± 51.60; LCL = 458.40, UCL = 561.60 12.4 The interval narrows as the sample size increases. 12.5 n s t x / 2 / a ± = 510 ± 2.009(200/ 50 ) = 510 ± 56.82; LCL = 453.18, UCL = 566.82 12.6 n s t x / 2 / a ± = 510 ± 2.009(75/ 50 ) = 510 ± 21.31; LCL = 488.69, UCL = 531.31 12.7 As the sample standard deviation decreases, the interval narrows. 12.8 n s t x / 2 / a ± = 510 ± 1.676(125/ 50 ) = 510 ± 29.63; LCL = 480.37, UCL = 539.63 12.9 n s t x / 2 / a ± = 510 ± 2.678(125/ 50 ) = 510 ± 47.34; LCL = 462.66, UCL = 557.34 12.10 As the confidence level increases the interval widens. 12.11 to 12.20 m : 0 H = 20 m : 1 H > 20 12.11 Rejection region: 19 , 05 . 1 , t t t n = > - a = 1.729 49 . 1 20 / 9 20 23 / = - = m - = n s x t , p-value = .0762 (Excel). There is not enough evidence to infer that the population mean is greater than 20. 12.12 Rejection region: 9 , 05 . 1 , t t t n = > - a = 1.833 05 . 1 10 / 9 20 23 / = - = m - = n s x t p-value = .1597 (Excel). There is not enough evidence to infer that the population mean is greater than 20. 188 12.13 Rejection region: » = > - a 49 , 05 . 1 , t t t n 1.676 36 . 2 50 / 9 20 23 / = - =

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m - = n s x t , p-value = .0112 (Excel). There is enough evidence to infer that the population mean is greater than 20. 12.14 As the sample size increases the test statistic increases [and the p-value decreases]. 12.15 Rejection region: 19 , 05 . 1 , t t t n = > - a = 1.729 68 . 2 20 / 5 20 23 / = - = m - = n s x t , p-value = .0074 (Excel). There is enough evidence to infer that the population mean is greater than 20. 12.16 Rejection region: 19 , 05 . 1 , t t t n = > - a = 1.729 67 . 20 / 29 20 23 / = - = m - = n s x t , p-value = .2552 (Excel). There is not enough evidence to infer that the population mean is greater than 20. 12.17 The t-statistic increases [and the p-value decreases] as the sample standard deviation decreases. 12.18 50 . 20 / 9 20 21 / = - = m - = n s x t , p-value = .3125 (Excel). There is not enough evidence to infer that the population mean is greater than 20. 12.19 98 . 2 20 / 9 20 26 / = - = m -
= n s x t , p-value = .0038 (Excel). There is enough evidence to infer that the population mean is greater than 20. 12.20 When the sample mean increases, the test statistic increases [and the p-value decreases]. 12.21 n s t x / 2 / a ± = 50 ± 2.262(15/ 10 ) = 50 ± 10.73; LCL = 39.27, UCL = 60.73 12.22 n z x / 2 / s ± a = 50 ± 1.96(15/ 10 ) = 50 ± 9.30; LCL = 40.70, UCL = 59.30 12.23 The student t distribution is more widely dispersed than the standard normal; thus, 2 / a z is smaller than 2 / a t . 189

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Chapter 12 - 187 Chapter 12 12.1 n s t x 2 a = 510...

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