Homework 08 Solutions

Homework 08 Solutions - CHEN3010 Applied Data Analysis Fall...

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CHEN3010 Applied Data Analysis Fall 2004 Homework 08 Solutions Problem 1 5-4. x 1 = 30.61 x 2 = 30.34 σ 1 = 0.10 σ 2 = 0.15 n 1 = 12 n 2 = 10 a) 90% two-sided confidence interval: ( ) ( ) x x z n n x x z n n 1 2 2 1 2 1 2 2 2 1 2 1 2 2 1 2 1 2 2 2 + + + α α σ σ μ μ σ σ / / ( ) 10 ) 15 . 0 ( 12 ) 10 . 0 ( 645 . 1 34 . 30 61 . 30 10 ) 15 . 0 ( 12 ) 10 . 0 ( 645 . 1 ) 34 . 30 61 . 30 ( 2 2 2 1 2 2 + + + μ μ 361 . 0 179 . 0 2 1 μ μ We are 90% confident that the mean fill volume for machine 1 exceeds that of machine 2 by between 0.179 and 0.361 fl. oz. b) 95% two-sided confidence interval: ( ) ( ) x x z n n x x z n n 1 2 2 1 2 1 2 2 2 1 2 1 2 2 1 2 1 2 2 2 + + + α α σ σ μ μ σ σ / / ( ) 10 ) 15 . 0 ( 12 ) 10 . 0 ( 96 . 1 34 . 30 61 . 30 10 ) 15 . 0 ( 12 ) 10 . 0 ( 96 . 1 ) 34 . 30 61 . 30 ( 2 2 2 1 2 2 + + + μ μ 379 . 0 161 . 0 2 1 μ μ We are 95% confident that the mean fill volume for machine 1 exceeds that of machine 2 by between 0.161 and 0.379 fl. oz. Comparison of parts a and b: As the level of confidence increases, the interval width also increases (with all other values held constant). c) 95% upper-sided confidence interval: ( ) μ μ σ σ α 1 2 1 2 1 2 1 2 2 2 + + x x z n n ( ) 10 ) 15 . 0 ( 12 ) 10 . 0 ( 645 . 1 34 . 30 61 . 30 2 2 2 1 + + μ μ 361 . 0 2 1 μ μ With 95% confidence, we believe the fill volume for machine 1 exceeds the fill volume of machine 2 by no more than 0.361 fl. oz. Problem 2 5-17. a) 1) The parameter of interest is the difference in mean etch rate, μ μ 1 2 2) H 0 : μ μ 1 2 0 = or μ μ 1 2 = 3) H 1 : μ μ 1 2 0 or μ μ 1 2 4) α = 0.05 5) The test statistic is t x x s n n p 0 1 2 0 1 2 1 1 = + ( )
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CHEN3010 Applied Data Analysis Fall 2004 6) Reject the null hypothesis if t 0 < + t n n α / , 2 2 1 2 where t 0 025 18 . , = 2.101 or t 0 > t n n α / , 2 2 1 2 + where t 0 025 18 . , = 2.101 7) x 1 = 9.97 x 2 = 10.4 0 = 0 s n s n s n n p = + + ( ) ( ) 1 1 2 2 2 2 1 2 1 1 2 s 1 = 0.422
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