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: ( ) ( ) xx z nn 12 2 1 2 1 2 2 2 12 12 2 1 2 1 2 2 2 −− + ≤−≤ − ++ αα σσ μμ // ( ) 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: ( ) ( ) 2 1 2 1 2 2 2 2 1 2 1 2 2 2 + ( ) 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: ( ) α 1 2 1 2 2 2 −≤ − ( ) 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, 2) H 0 : 0 = or = 3) H 1 : 0 −≠ or 4) α = 0.05 5) The test statistic is t xx s p 0 12 0 11 = + ()
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CHEN3010 Applied Data Analysis Fall 2004 6) Reject the null hypothesis if t 0 < + t nn α /, 22 12 where t 0025 18 ., = 2.101 or t 0 > t α + where t = 2.101 7) x 1 = 9.97 x 2 = 10.4 0 = 0 s ns p = + + () 11 2 2 2 s 1 = 0.422 s 2 = 0.231 = + = 10 0422 10 0 231 18 0 340 (.
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This note was uploaded on 10/11/2011 for the course CHEN 3010 taught by Professor Kompala,dh during the Spring '08 term at Colorado.

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

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