10 STAT HWA a - Dr. V.R. Bencivenga Economics 329 Practice...

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Unformatted text preview: Dr. V.R. Bencivenga Economics 329 Practice Assignment #10A: Right Answers 1. X X i p y probabilit success with Bernoulli iid n ,..., 1 i , X (chemicals) Y Y j p y probabilit success with Bernoulli iid n ,..., 1 j , Y (no chemicals) Y X p p : H Y X A p p : H 05 . There are two alternative correct sampling distributions that can be used to derive the rejection regions: (1) ) 1 , ( N ~ n 1 n 1 p 1 p ) p p ( p p Y X Y X Y X by the CLT, since 30 n X and 398 n Y are large and where Y X n n Y X p (2) ) 1 , ( N ~ n p 1 p n p 1 p ) p p ( p p Y Y Y X X X Y X Y X by the CLT, where X X n X p and Y Y n Y p Reject H if 1 Y X cv p p or if 2 Y X cv p p . Find 1 cv and 2 cv such that: 025 . p p | cv p p P Y X 1 Y X and 025 . p p | cv p p P Y X 2 Y X Using (1) 025 . 398 1 30 1 168 . 1 168 . cv n 1 n 1 p 1 p ) p p ( p p P 1 Y X Y X Y X where 168 . 398 30 62 10 p 025 . 96 . 1 Z P 96 . 1 398 1 30 1 168 . 1 168 . cv 1 139 . cv 1 Because of the symmetry of the normal distribution, we know that 2 cv is the same distance below zero (the value of Y X p p if H is true) as 1 cv is above zero. Therefore, 139 . cv 2 . This would be verified by calculating 2 cv from 025 . 398 1 30 1 168 . 1 168 . cv n 1 n 1 p 1 p ) p p ( p p P 2 Y X Y X Y X 2 Since 139 . 177 . 156 . 333 . 398 62 30 10 p p Y X , reject H Alternatively, using (2) 025 . 398 156 . 1 156 . 30 333 . 1 333 . cv n p 1 p n p 1 p ) p p ( p p P 1 Y Y Y X X X Y X Y X which uses 333 . 30 10 p X and 156 . 398 62 p Y . 025 . 96 . 1 Z P . Therefore 96 . 1 398 156 . 1 156 . 30 333 . 1 333 . cv 1 172 . 398 156 . 1 156 . 30 333 . 1 333 . 96 . 1 cv 1 Because of the symmetry of the normal distribution 172 . cv 2 . Since 172 . 177 . p p Y X , reject H . Note that both (1) and (2) are correct, but the rejection regions they yield are quite different!...
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This note was uploaded on 02/26/2012 for the course ECONOMICS 329 taught by Professor Bencivenga during the Spring '12 term at University of Texas at Austin.

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10 STAT HWA a - Dr. V.R. Bencivenga Economics 329 Practice...

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