Unformatted text preview: y = 103 of the patients had new STDs. Construct and interpret a 95% AgrestiCoull conﬁdence interval for the probability of contracting an STD within six months after counseling (as in the study). Answer: From pp. 207–208, ˜ p = y + 2 n + 4 = 103 + 2 1438 + 4 = 105 1442 = 0 . 0728 . SE ˜ p = r ˜ p (1˜ p ) n + 4 = r . 0728(1. 0728) 1442 = 0 . 0068 . So a 95% CI for for the probability of contracting an STD after counseling is ˜ p ± 1 . 96 SE ˜ p = 0 . 0728 ± 1 . 96(0 . 0068) = 0 . 0728 ± . 0133 = (0 . 0595 , . 0861) . We are 95% conﬁdent that the true probability of contracting an STD after counseling is between 5.95% and 8.61%. Your book’s solution to 6.48 rounds to three decimal places instead of four; either is ﬁne....
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 Fall '09
 Hendrix
 Human sexual behavior

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