420Hw09ans - STAT 420 (10 points) (due Friday, November 2,...

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STAT 420 Fall 2007 Homework #9 (10 points) (due Friday, November 2, by 4:00 p.m.) 1. Prove ( ) ( ) ( ) = = = = = - + - = - I i I i I i i n j i ij i i i n j ij y y y y n y y 1 1 2 1 2 1 1 2 . ( ) ( ) = = = = - + - = - I i n j i i ij I i n j ij i i y y y y y y 1 1 2 1 1 2 = ( ) ( ) ( ) ( ) = = = = = = - + - - + - I i n j i I i n j i i ij I i n j i ij i i i y y y y y y y y 1 1 2 1 1 1 1 2 2 = ( ) ( ) ( ) ( ) = = = = = = - + - - + - I i n j i I i n j i ij i I i n j i ij i i i y y y y y y y y 1 1 2 1 1 1 1 2 2 . Since ( ) = - i n j i ij y y 1 = 0, i = 1, … , I , ( ) ( ) = = - - I i n j i ij i i y y y y 1 1 2 = 0, and ( ) ( ) ( ) = = = = = = - + - = - I i n j i I i n j i ij I i n j ij i i i y y y y y y 1 1 2 1 1 2 1 1 2 .
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2. A transportation analyst wishes to compare the “degree of support” for a new rapid transit system among the following three groups of people in the Madison, Wisconsin, area: group A, University of Wisconsin faculty; group B, downtown businessmen; and group C, state government personnel. A questionnaire was designed from which a “rapid transit support index” could be computed for each respondent. The questionnaire was given to randomly selected people from each group. The results follow. Rapid Transit Support Index Group A B C 66 59 70 65 76 84 45 53 62 72 78 50 57 49 61 53 72 80 Stating any assumptions you make, test for differences between the three populations represented by the three samples using the F test. Specify the null and the alternative hypotheses. Show the calculations leading to your conclusion in the form of an
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420Hw09ans - STAT 420 (10 points) (due Friday, November 2,...

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