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# quiz7_key - y = 103 of the patients had new STDs Construct...

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NAME: Stat 205 Quiz 7 1. (5 points) As part of a study of the treatment of anemia in cattle, researchers measured the concentration of selenium in the blood of n = 36 cows who had been given a daily selenium supplement. The mean selenium concentration was 6.21 μ g/dL and the standard deviation was 1.84 μ g/dL. Construct and interpret a 95% confidence interval for the population mean. Answer: We have ¯ y = 6 . 21 , s = 1 . 84 and n = 36 . Here, α = 0 . 05 and from the table on the back cover of your book, t 0 . 025 (35) 2 . 04 (I rounded up to df = 30 to be conservative). So the confidence interval is ¯ y ± t 0 . 025 (35) s n = 6 . 21 ± 2 . 04(1 . 84 / 36) = 6 . 21 ± 0 . 6256 = (5 . 58 , 6 . 84) , same as in your homework solutions for 6.19. We are 95% confident that the true mean selenium level of all cows treated with the supple- ment is between 5.58 and 6.84 g/dL. 2. (5 points) A group of n = 1438 sexually active patients were counseled on condom use and the risk of contracting a sexually transmitted disease (STD). After six months
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Unformatted text preview: y = 103 of the patients had new STDs. Construct and interpret a 95% Agresti-Coull 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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