Chapter 10 - 160 Chapter 10 10.1 An unbiased estimator of a...

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Chapter 10 10.1 An unbiased estimator of a parameter is an estimator whose expected value equals the parameter. 10.2 10.3 10.4 An unbiased estimator is consistent if the difference between the estimator and the parameter grows smaller as the samp le size grows. 10.5 The mean is consistent because it is unbiased and the standard error grows smaller as n increases. 10.6 10.7 If there are two unbiased estimators of a parameter, the one whose variance is smaller is relatively efficient. 161 10.8 10.9 n z x / 2 / s ± a = 100 ± 1.96(25/ 50 ) = 100 ± 6.93; LCL = 93.07, UCL = 106.93 10.10 n z x / 2 / s ± a = 100 ± 1.645(25/ 50 ) = 100 ± 5.82; LCL = 94.18, UCL = 105.82 10.11 n z x / 2 / s ± a = 100 ± 2.575(25/ 50 ) = 100 ± 9.11; LCL = 90.89, UCL = 109.11 10.12 The interval widens. 10.13 n z x / 2 / s ± a = 100 ± 1.96(10/ 50 ) = 100 ± 2.77; LCL = 97.23, UCL = 102.77 10.14 n z x / 2 / s ± a = 100 ± 1.96(50/ 50 ) = 100 ± 13.86; LCL = 86.14, UCL = 113.86 10.15 The interval widens. 10.16 n z x / 2 / s ± a = 100 ± 1.96(25/ 25 ) = 100 ± 9.80; LCL = 90.20, UCL = 109.80 10.17 n z x / 2 / s ± a = 100 ± 1.96(25/ 400 ) =100 ± 2.45; LCL = 97.55, UCL = 102.45 10.18 The interval narrows. 10.19 n z x / 2 / s ± a = 30 ± 1.96(25/ 50 ) = 30 ± 6.93; LCL = 23.07, UCL = 36.93 10.20 n z x / 2 / s ± a = 200 ± 1.96(25/ 50 ) = 200 ± 6.93; LCL = 193.07, UCL = 206.93 10.21 The width of the interval is unchanged. 10.22 n z x / 2 / s ± a = 500 ± 1.645(12/ 50 ) = 500 ± 2.79; LCL = 497.21, UCL = 502.79 162 10.23 n z x / 2 / s ± a = 500 ± 1.96(12/ 50 ) = 500 ± 3.33; LCL = 496.67, UCL = 503.33 10.24 n z x / 2 / s ± a = 500 ± 2.575(12/ 50 ) = 500 ± 4.37; LCL = 495.63, UCL = 504.37 10.25 The interval narrows. 10.26 n z x / 2 / s ± a = 500 ± 1.645(10/ 50 =500 ± 2.33; LCL = 497.67, UCL = 502. .33 10.27 n z x / 2 / s ± a = 500 ± 1.645(14/ 50 =500 ± 3.26; LCL = 496.74, UCL = 503.26 10.28 The interval narrows. 10.29 n z x / 2 / s ± a = 500 ± 1.645(12/ 100 ) = 500 ± 1.97; LCL = 498.03, UCL = 501.97 10.30 n z x / 2 / s ± a = 500 ± 1.645(12/ 200 ) = 500 ± 1.40; LCL = 498.60, UCL = 501.40 10.31 The interval widens. 10.32 n z x / 2 / s ± a = 100 ± 1.645(12/ 50 ) = 100 ± 2.79; LCL = 97.21, UCL
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Chapter 10 - 160 Chapter 10 10.1 An unbiased estimator of a...

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