sol4 - Problem 294/12 (a) The parameter of interest is...

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Unformatted text preview: Problem 294/12 (a) The parameter of interest is =true average braking distance at 40 mph for the new design . The hypothesis are H : = 120 vs H a : < 120. (b) E ( x ) ( = 120 , if H is true, < 120 , if H a is true. Hence R 2 should be used. (c) X = n = 10 6 = 1 . 6667, so = P ( R 2 when H is true) = P ( X 155 . 20when = 120) = P ( X- 120 1 . 6667 115 . 20- 120 1 . 6667 ) = N (- 2 . 88; 0 , 1) = 0 . 002 . To obtain = 0 . 001, we need to replace 115.20 by a number c such that P ( X c when = 120) = N ( c ; = 120 , X = 1 . 6667) = 0 . 001. Hence, we use JMP to compute c = Normal Quantile(0.001,120,1.667) = 114 . 87. (d) P (accepting H when = 115) = P ( X 115 . 20when = 115) = P ( X- 115 1 . 6667 115 . 20- 115 1 . 6667 ) = 1- N (0 . 12; 0 , 1) = 0 . 4522. For the first region, = P ( Z - 2 . 33) = N (- 2 . 33; 0 , 1) = 0 . 01. For the second region, = P ( Z - 2 . 88) = 0 . 002. Problem 305/24 = true average viscosity. H : = 3000 vs H a : 6 = 3000. t obs = x- 3000 s/ n = 2887 . 6- 3000 84 / 5 =- 2 . 99. At level , the rejection region is | t obs | = 2 . 99 > t 2 , 4 . For example, using the table below, we can see that we reject at = 0 . 05 but dont reject at = 0 . 01. Hence, the requirement is not satisfied at = 0 . 05. On the other hand, theres no evidence that indicates that the requirement is satisfied at = 0 . 01. (For the homework, it suffices to report the test for your favorite choice of ). 1 Problem 311/44 p = proportion of defectives, by robots. H : p = 0 . 035 vs H a : p < . 035. We use z obs = p- . 035 (0 . 035)(0 . 965) / 500 = z obs = 15 500- . 035 (0 . 035)(0 . 965) / 500 =- . 005 . 0082 =- . 61....
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This note was uploaded on 09/09/2008 for the course ENGRD 2700 taught by Professor Staff during the Summer '05 term at Cornell University (Engineering School).

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sol4 - Problem 294/12 (a) The parameter of interest is...

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