H524e-PS8-Solutions

# H524e-PS8-Solutions - Readings from the textbook Chapters...

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Readings from the textbook Chapters 15 & 16 Problems to be turned in for grading Chapter 15: 8 (hint: part c is asking you to use the methods from week 7) (10 points) a. H 0 = P 1 = P 2 : The population proportion of students who drove while drinking is the same in the two calendar years (before and after the legal drinking age was raised). H a = P 1 ≠ P 2 : The population proportion of students who drove while drinking is different in the two calendar years (before and after the legal drinking age was raised). Pearson chi2(1) = 55.3553 Pr = 0.000 Total 2,637 2,657 5,294 2 1,387 1,666 3,053 1 1,250 991 2,241 row 1 2 Total col . tabi 1250 991 \ 1387 1666, chi2 The p-value is 0.000, so we reject the null. We can accept the alternative hypotheses that driving while drinking was different in the two calendar years. b. We recognize that in the two years (1983 and 1987), there was a change in the behavior of college-age drinking while driving. c. ^ p 1 = x 1 n 1 , ^ p 2 = x 2 n 2 ^ p 1 = 1250 2637 = 0.47 , ^ p 2 = 991 2657 = 0.37

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( 1 n 1 ) +( 1 n 2 ) ¿ ^ p ( 1 ^ p ) ¿ ¿ z = ( ^ p 1 ^ p 2 ) ( p 1 p 2 ) ¿ ¿ ( .47 .37 ) .42 ( .58 ) 2637 +( .42 ( .58 ) 2657 ) .000184 ¿ 0.1 ¿ ¿ ¿ 7.37 7.37 > 1.96, so, like the Chi-square test, we reach the same conclusion and reject the null. d. ^ p 1 ( 1 ^ p 1 ) n 1 + ^ p 2 ( 1 ^ p 2 ) n 2 ( ^ p 1 ^ p 2 ) + z a 2 = ¿¿ .47 ( .53 ) 2637 + .37 ( .63 ) 2657 0.1 ± 1.96 = ¿¿ 0.1 ± 1.96 = .0001822 0.1 ± .026 CI = (0.074, 0.126) e. The CI does not contain 0, and I would not have expected it to since the null was rejected.
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