# ismch08 - Chapter 8 Estimation 113 Chapter 8 Estimation 8.1...

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Unformatted text preview: Chapter 8: Estimation 113 Chapter 8: Estimation 8.1 a. An unbiased point estimator of the population mean is the sample mean: i X X n = = ∑ 520.95 Results for: Sugar.xls Descriptive Statistics: Weights Variable N Mean Median TrMean StDev SE Mean Weights 100 520.95 518.75 520.52 9.45 0.95 Variable Minimum Maximum Q1 Q3 Weights 504.70 544.80 513.80 527.28 b. Evidence of non-normality? P-Value: 0.000 A-Squared: 1.989 Anderson-Darling Normality Test N: 100 StDev: 9.45150 Average: 520.948 545 535 525 515 505 .999 .99 .95 .80 .50 .20 .05 .01 .001 Probability Weights Normal Probability Plot The distribution shows evidence of non-normality c. The unbiased point estimate of the variance of the sample mean: 2 2 (9.45) ( ) .8930 100 s Var X n = = = 114 Instructor’s Solutions Manual for Statistics for Business & Economics, 5 th Edition 8.2 a. Evidence of non-normality? P-Value: 0.837 A-Squared: 0.194 Anderson-Darling Normality Test N: 8 StDev: 14.2020 Average: 101.375 125 115 105 95 85 .999 .99 .95 .80 .50 .20 .05 .01 .001 Probability HousePrice8_ Normal Probability Plot No evidence of non-normality. b. The minimum variance unbiased point estimator of the population mean is the sample mean: i X X n = = ∑ 101.375 c. The unbiased point estimate of the variance of the sample mean: 2 2 2 2 83627 8(101.375) 201.6964 1 7 i x x nx s n-- = = =- ∑ 2 2 201.6964 ˆ ( ) ; ( ) 25.2121 8 x x s Var X Var X n n σ = = = = d. 3 .375 8 x x p n = = = Chapter 8: Estimation 115 8-3 a. Check each variable for normal distribution: P-Value: 0.318 A-Squared: 0.413 Anderson-Darling Normality Test N: 30 StDev: 2.46842 Average: 50.1 55 50 45 .999 .99 .95 .80 .50 .20 .05 .01 .001 Probability Meals Normal Probability Plot P-Value: 0.383 A-Squared: 0.377 Anderson-Darling Normality Test N: 25 StDev: 2.50466 Average: 21.24 25 20 15 .999 .99 .95 .80 .50 .20 .05 .01 .001 Probability Attendance Normal Probability Plot 116 Instructor’s Solutions Manual for Statistics for Business & Economics, 5 th Edition P-Value: 0.126 A-Squared: 0.569 Anderson-Darling Normality Test N: 25 StDev: 1.96384 Average: 12.24 16 15 14 13 12 11 10 9 .999 .99 .95 .80 .50 .20 .05 .01 .001 Probability Ages Normal Probability Plot No evidence of non-normality in Meals, Attendance or Ages b. Unbiased estimates of population mean and variance: Descriptive Statistics: Meals, Attendance, Ages Variable N Mean Median TrMean StDev SE Mean Meals 30 50.100 50.000 50.192 2.468 0.451 Attendan 25 21.240 21.000 21.348 2.505 0.501 Ages 25 12.240 12.000 12.217 1.964 0.393 Variable Minimum Maximum Q1 Q3 Meals 45.000 55.000 48.000 52.000 Attendan 15.000 25.000 19.500 23.500 Ages 9.000 16.000 10.000 14.000 Variable Unbiased estimate of mean Unbiased estimate of variance (s 2 ) Meals 50.100 (2.468) 2 = 6.0910 Attendance 21.240 (2.505) 2 = 6.2750 Ages 12.240 (1.964) 2 = 3.8573 8-4 a....
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ismch08 - Chapter 8 Estimation 113 Chapter 8 Estimation 8.1...

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