MBS-ProblemSolutions-Ch10

# MBS-ProblemSolutions-Ch10 - Chapter 10 Statistical...

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Unformatted text preview: Chapter 10 Statistical Inference About Means and Proportions with Two Populations Learning Objectives 1. Be able to develop interval estimates and conduct hypothesis tests about the difference between two population means when 1 σ and 2 σ are known. 2. Know the properties of the sampling distribution of 1 2 x x- . 3. Be able to use the t distribution to conduct statistical inferences about the difference between two population means when 1 σ and 2 σ are unknown. 4. Learn how to analyze the difference between two population means when the samples are independent and when the samples are matched. 5. Be able to develop interval estimates and conduct hypothesis tests about the difference between two population proportions. 6. Know the properties of the sampling distribution of 1 2 p p- . Solutions: 10 - 1 Chapter 10 1. a. x x 1 2- = 13.6 - 11.6 = 2 b. / 2 .05 z z α = = 1.645 2 2 1 2 1 2 1 2 1.645 x x n n σ σ- ± + 2 2 (2.2) (3) 2 1.645 50 35 ± + 2 ± .98 (1.02 to 2.98) c. / 2 .025 z z α = = 1.96 2 2 (2.2) (3) 2 1.96 50 35 ± + 2 ± 1.17 (.83 to 3.17) 2. a. ( 29 1 2 2 2 2 2 1 2 1 2 (25.2 22.8) 2.03 (5.2) 6 40 50 x x D z n n σ σ---- = = = + + b. p-value = 1.0000 - .9788 = .0212 c. p-value ≤ .05, reject H . 3. a. ( 29 1 2 2 2 2 2 1 2 1 2 (104 106) 1.53 (8.4) (7.6) 80 70 x x D z n n σ σ---- = = = - + + b. p-value = 2(.0630) = .1260 c. p-value > .05, do not reject H . 4. a. 1 2 x x- = 2.04 - 1.72 = .32 b. 2 2 1 2 .025 1 2 z n n σ σ + 2 2 (.10) (.08) 1.96 1.96(.0208) .04 40 35 + = = c. .32 ± .04 (.28 to .36) 5. a. 1 2 x x- = 135.67 – 68.64 = 67.03 10 - 2 Statistical Inference About Means and Proportions with Two Populations b. 2 2 2 2 1 2 / 2 1 2 (35) (20) 2.576 17.08 40 30 z n n α σ σ + = + = c. 67.03 ± 17.08 (49.95 to 84.11) We estimate that men spend \$67.03 more than women on Valentine’s Day with a margin of error of \$17.08. 6. 1 μ = Mean loan amount for 2002 2 μ = Mean loan amount for 2001 H : 1 2 μ μ- ≤ H a : 1 2 μ μ- ( 29 1 2 2 2 2 2 1 2 1 2 (175 165) 2.17 55 50 270 250 x x D z n n σ σ---- = = = + + p-value = 1.0000 - .9850 = .0150 p-value ≤ .05; reject H . The mean loan amount has increased between 2001 and 2002. 7. a. 1 μ = Population mean 2002 2 μ = Population mean 2003 H : 1 2 μ μ- ≤ H a : 1 2 μ μ- b. With time in minutes, 1 2 x x- = 172 - 166 = 6 minutes c. ( 29 1 2 2 2 2 2 1 2 1 2 (172 166) 2.61 12 12 60 50 x x D z n n σ σ---- = = = + + p-value = 1.0000 - .9955 = .0045 p-value ≤ .05; reject H . The population mean duration of games in 2003 is less than the population mean in 2002. d. 2 2 1 2 1 2 .025 1 2 x x z n n σ σ- ± + 10 - 3 Chapter 10 2 2 12 12 (172 166) 1.96 60 50- ± + 6 ± 4.5 (1.5 to 10.5) e. Percentage reduction: 6/172 = 3.5%. Management should be encouraged by the fact that steps taken in 2003 reduced the population mean duration of baseball games. However, the statistical analysis shows that the reduction in the mean duration is only 3.5%. The interval estimate shows the reduction in the population mean is 1.5 minutes (.9%) to 10.5 minutes (6.1%). Additional data reduction in the population mean is 1....
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MBS-ProblemSolutions-Ch10 - Chapter 10 Statistical...

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