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# Ch10 - Chapter 10 Statistical Inference about Means and...

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10 - 1 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 .

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Chapter 10 10 - 2 Solutions: 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. ( ) 1 2 0 2 2 2 2 1 2 1 2 (25.2 22.8) 0 2.03 (5.2) 6 40 50 x x D z n n σ σ = = = + + b. p -value = .5000 - .4788 = .0212 c. p -value .05, reject H 0 . 3. a. ( ) 1 2 0 2 2 2 2 1 2 1 2 (104 106) 0 1.53 (8.4) (7.6) 80 70 x x D z n n σ σ = = = − + + b. p -value = 2(.5000 - .4370) = .1260 c. p -value > .05, do not reject H 0 . 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)
Statistical Inference about Means and Proportions with Two Populations 10 - 3 5. a. 1 2 x x = 14.9 - 10.3 = 4.6 years b. 2 2 2 2 1 2 / 2 1 2 (5.2) (3.8) 1.96 1.3 100 85 z n n α σ σ + = + = c. 4.6 ± 1.3 (3.3 to 5.9) 6. 1 µ = Mean loan amount for 2002 2 µ = Mean loan amount for 2001 H 0 : 1 2 0 µ µ H a : 1 2 0 µ µ > ( ) 1 2 0 2 2 2 2 1 2 1 2 (175 165) 0 2.17 55 50 270 250 x x D z n n σ σ = = = + + p -value = .5000 - .4850 = .0150 p -value .05; reject H 0 . The mean loan amount has increased between 2001 and 2002. 7. a. H 0 : 1 2 0 µ µ = H a : 1 2 0 µ µ b. ( ) 1 2 0 2 2 2 2 1 2 1 2 (40 35) 0 2.41 9 10 36 49 x x D z n n σ σ = = = + + p -value = 2(.5000 - .4920) = .0160 p -value .05; reject H 0 . There is a difference between the population mean ages at the two stores. 8. a. ( ) 1 2 2 2 2 2 1 2 1 2 0 (69.95 69.56) 0 1.08 2.5 2.5 112 84 x x z n n σ σ = = = + + b. p -value = 2(.5000 - .3599) = .2802 c. p -value > .05; do not reject H 0 . Cannot conclude that there is a difference between the population mean scores for the two golfers.

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Chapter 10 10 - 4 9. a. 1 2 x x = 22.5 - 20.1 = 2.4 b. 2 2 2 2 2 2 1 2 1 2 2 2 2 2 2 2 2 2 1 2 1 1 2 2 2.5 4.8 20 30 45.8 1 2.5 1 4.8 1 1 19 20 29 30 1 1 s s n n df s s n n n n + + = = = + + Use df = 45. c. t .025 = 2.014 2 2 2 2 1 2 .025 1 2 2.5 4.8 2.014 2.1 20 30 s s t n n + = + = d. 2.4 ± 2.1 (.3 to 4.5) 10. a. ( ) 1 2 2 2 2 2 1 2 1 2 0 (13.6 10.1) 0 2.18 5.2 8.5 35 40 x x t s s n n = = = + + b. 2 2 2 2 2 2 1 2 1 2 2 2 2 2 2 2 2 2 1 2 1 1 2 2 5.2 8.5 35 40 65.7 1 5.2 1 8.5 1 1 34 35 39 40 1 1 s s n n df s s n n n n + + = = = + + Use df = 65 c. Using t table, area in tail is between .01 and .025 two-tail p -value is between .02 and .05.
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Ch10 - Chapter 10 Statistical Inference about Means and...

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