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ISM_Chapter_10 - Chapter 10 10.1 A point estimator is a...

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Chapter 10 10.1 A point estimator is a single value; an interval estimator is a range of values. 10.2 An unbiased estimator of a parameter is an estimator whose expected value equals the parameter. 10.3 10.4 10.5 An unbiased estimator is consistent if the difference between the estimator and the parameter grows smaller as the sample size grows. 10.6 207
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10.7 If there are two unbiased estimators of a parameter, the one whose variance is smaller is relatively efficient. 10.8 10.9 a. n / z x 2 / σ ± α = 100 ± 1.645(25/ 50 ) = 100 ± 5.82; LCL = 94.18, UCL = 105.82 b. n / z x 2 / σ ± α = 100 ± 1.96(25/ 50 ) = 100 ± 6.93; LCL = 93.07, UCL = 106.93 c. n / z x 2 / σ ± α = 100 ± 2.575(25/ 50 ) = 100 ± 9.11; LCL = 90.89, UCL = 109.11 d. The interval widens. 10.10 a. n / z x 2 / σ ± α = 200 ± 1.96(50/ 25 ) = 200 ± 19.60; LCL = 180.40, UCL = 119.60 b. n / z x 2 / σ ± α = 200 ± 1.96(25/ 25 ) = 200 ± 9.80; LCL = 190.20, UCL = 209.80 c. n / z x 2 / σ ± α = 200 ± 1.96(10/ 25 ) = 200 ± 3.92; LCL = 196.08, UCL = 203.92 d. The interval narrows. 10.11 a. n / z x 2 / σ ± α = 80 ± 1.96(5/ 25 ) = 80 ± 1.96; LCL = 78.04, UCL = 81.96 b. n / z x 2 / σ ± α = 80 ± 1.96(5/ 100 ) = 80 ± .98; LCL = 79.02, UCL = 80.98 c. n / z x 2 / σ ± α = 80 ± 1.96(5/ 400 ) = 80 ± .49; LCL = 79.51, UCL = 80.49 d. The interval narrows. 10.12 a. n / z x 2 / σ ± α = 500 ± 2.33(12/ 50 ) = 500 ± 3.95; LCL = 496.05, UCL = 503.95 b. n / z x 2 / σ ± α = 500 ± 1.96(12/ 50 ) = 500 ± 3.33; LCL = 496.67, UCL = 503.33 c. n / z x 2 / σ ± α = 500 ± 1.645(12/ 50 ) = 500 ± 2.79; LCL = 497.21, UCL = 502.79 d. The interval narrows. 208
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10.13 a. n / z x 2 / σ ± α = 500 ± 2.575(15/ 25 ) = 500 ± 7.73; LCL = 492.27, UCL = 507.73 b. n / z x 2 / σ ± α = 500 ± 2.575(30/ 25 ) = 500 ± 15.45; LCL = 484.55, UCL = 515.45 c. n / z x 2 / σ ± α = 500 ± 2.575(60/ 25 ) = 500 ± 30.91; LCL = 469.09, UCL = 530.91 d. the interval widens. 10.14 a. n / z x 2 / σ ± α = 10 ± 1.645(5/ 100 ) = 10 ± .82; LCL = 9.18, UCL = 10.82 b. n / z x 2 / σ ± α = 10 ± 1.645(5/ 25 ) = 10 ± 1.64; LCL = 8.36, UCL = 11.64 c. n / z x 2 / σ ± α = 10 ± 1.645(5/ 10 ) = 10 ± 2.60; LCL = 7.40, UCL = 12.60 d. The interval widens. 10.15 a. n / z x 2 / σ ± α = 100 ± 1.96(20/ 25 ) = 100 ± 7.84; LCL = 92.16, UCL = 107.84 b. n / z x 2 / σ ± α = 200 ± 1.96(20/ 25 ) = 200 ± 7.84; LCL = 192.16, UCL = 207.84 c. n / z x 2 / σ ± α = 500 ± 1.96(20/ 25 ) = 500 ± 7.84; LCL = 492.16, UCL = 507.84 d. The width of the interval is unchanged.
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