quiz9Sp2011_key

quiz9Sp2011_key - include zero. (c) log = log 164 178 130...

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NAME: Stat 205 Quiz 9 Take-Home Quiz due by beginning of class, Thursday April 21 A case-control study was designed to examine risk factors for cervical dysplasia (Becker et al., 1994); the women in the study were patients aged 18 to 40. There were n 1 = 175 cases with cervical dysplasia and n 2 = 308 controls without. Each woman was tested for human papilloma virus (HPV) and either positive (HPV + ) or negative (HPV - ): dysplasia no dysplasia HPV + 164 130 HPV - 11 178 total 175 308 Let p 1 be the probability of HPV + among the cases and p 2 be the probability of HPV + among the controls. (a) ˆ p 1 = 164 175 = 0 . 937 , ˆ p 2 = 130 308 = 0 . 422 , ˆ p 1 - ˆ p 2 = 0 . 515 , ˆ p 1 ˆ p 2 = 2 . 22 , ˆ θ = ˆ p 1 / (1 - ˆ p 1 ) ˆ p 2 / (1 - ˆ p 2 ) = 20 . 4 . The probability of being HPV + increases by one half when dysplasia is present. One is twice as likely to have HPV when dysplasia is present. The odds of being HPV + increase by a factor of 20 when dysplasia is present. (b) ˜ p 1 = 164 + 1 175 + 2 = 0 . 932 , ˜ p 2 = 130 + 1 308 + 2 = 0 . 423 , SE ˜ p 1 - ˜ p 2 = s ˜ p 1 (1 - ˜ p 1 ) n 1 + 2 + ˜ p 2 (1 - ˜ p 2 ) n 2 + 2 = 0 . 0338 . ˜ p 1 - ˜ p 2 ± 1 . 96 SE ˜ p 1 - ˜ p 2 = (0 . 443 , 0 . 576) . We reject that H 0 : p 1 = p 2 at the 5% level because the 95% confidence interval does not
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Unformatted text preview: include zero. (c) log = log 164 178 130 11 = log 20 . 4 = 3 . 02 . SE log = r 1 y 1 + 1 n 1-y 1 + 1 y 2 + 1 n 2-y 2 = r 1 164 + 1 11 + 1 130 + 1 178 = 0 . 332 . The 95% condence interval for log is given by 3 . 02 1 . 96 . 332 = (2 . 37 , 3 . 67) . The 95% condence interval for is given by ( e 2 . 37 ,e 3 . 67 ) = (10 . 6 , 39 . 1) . The odds of dysplasia increase by 10 to 40 times for HPV + versus HPV-. Also , the odds of HPV + increase 10 to 40 times for those with dysplasia versus those without. (d) We reject H : = 1 at the 5% level because the 95% condence interval does not include one. This agrees with part (b). (e) There is a signicant association between dysplasia and HPV; we reject no association at the 5% level in parts (b) and (d)....
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quiz9Sp2011_key - include zero. (c) log = log 164 178 130...

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