HW2_Sol - STAT 426 HW2. 2.8 Let p 1 be the probability that...

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Unformatted text preview: STAT 426 HW2. 2.8 Let p 1 be the probability that a subject would be referred for heart catheter- ization for blacks, and p 2 be the probability that a subject would be referred for heart catheterization for whites. p 1 = 0 . 847 ,p 2 = 0 . 906 a The odds of referral for cardiac catheterization for blacks (odds(blacks))= p 1 / (1- p 1 ) = 0 . 847 / (1- . 847) = 5 . 54; The odds of referral for cardiac catheterization for whites (odds(white))= p 2 / (1- p 2 ) = 0 . 906 / (1- . 906) = 9 . 64 . The odds ratio=odds(blacks)/odds(whites)=5.54/9.64=57%. b Odds ratio is NOT the ratio of two probabilities. In fact, it is the ratio of two odds. Relative risk is the ratio of two probabilities. Here, relative risk= p 1 /p 2 = . 847 / . 906 = 93% . Therefore, the correct percentage for this interpretation is 93. 2.10 Let B denotes blacks, W denotes whites, X denotes race of murder, and Y denotes race of victim. P (X=B | Y=B) = 0 . 91 ,P (X=W | Y=W) = 0 . 83 . a These statistics refer to X given Y. 1 b X Y B W B n 11 n 12 W n 21 n 22 odds ratio= n 11 /n 12 n 21 /n 22 = . 91 / (1- . 91) (1- . 83) / . 83 = 49 . 37 The odds of a black person killing a black person is about 49.73 times the odds of a black person killing a white person. c P (Y=W | X=W) = P (X=W | Y=W) P (Y=W) P (X=W | Y=W) P (Y=W) + P (X=W | Y=B) P (Y=B) = . 83 P (Y=W) . 83 P (Y=W) + (1- . 91) P (Y=B) = . 83 P (Y=W) . 83 P (Y=W) + (1- . 91)(1- P (Y=W)) We need to know P ( Y = W ) (or P ( Y = B )) to estimate this probability. 2.19 Democrat Independence Republican White 871 (982.21) 444(438.77) 873 (767.01) Black 302 (190.79) 80 (85.23) 43 (148.99) a χ 2 = (871- 982 . 21) 2 982 . 21 + ... + (43- 148 . 99) 2 148 . 99 = 167 . 85 (p-value < . 0001) G 2 = 2[871 log( 871 982 . 21 ) + ... + 43 log( 43 148 . 99 )] = 187 . 58 (p-value...
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This note was uploaded on 04/29/2010 for the course STAT stat 426 taught by Professor Xe during the Spring '10 term at University of Illinois at Urbana–Champaign.

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HW2_Sol - STAT 426 HW2. 2.8 Let p 1 be the probability that...

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