{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

quiz9Sp2011_key

# quiz9Sp2011_key - include zero(c log ˆ θ = log 164 × 178...

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: include zero. (c) log ˆ θ = log 164 × 178 130 × 11 = log 20 . 4 = 3 . 02 . SE log ˆ θ = 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% conﬁdence interval for log θ is given by 3 . 02 ± 1 . 96 × . 332 = (2 . 37 , 3 . 67) . The 95% conﬁdence interval for θ 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 : θ = 1 at the 5% level because the 95% conﬁdence interval does not include one. This agrees with part (b). (e) There is a signiﬁcant association between dysplasia and HPV; we reject no association at the 5% level in parts (b) and (d)....
View Full Document

{[ snackBarMessage ]}