Question

tal of 475 In a study of HIV infection among women entering the New York State prison system, a to inmates were cross-classified with respect to HIV seropositivity and their histories of intra 2. use. HIV Seropositivity Negative 27 Total 339 136 Positive 312 IV Drug User es 33788175 No Total who are not IV Among women who are IV drug users, what proportion is HIV positive? Among women drug users, what proportion is HIV positive? a. 3120.42 04 2-5 · 0-55 IS 13L 3 34 b. At the 0.01 level of significance, test to determine if the proportion of HIV positive is lower in non-IV drug users than IV drug users. Ho: ii. Significance level: 0,o iii. p-value: iv. Conclusion: What can you say about the proportion of HIV positive between IV drug users and non-users? v. Calculate the 95% confidence interval estimate for the difference in the two population proportions of HIV positive between IV drug users and non-users. i. Point estimate of the difference in the two proportions: c ii. Confidence Interval Estimate: ii. What can be said about the difference in the two population proportions?

Answer 1

(b)

(i)

Ho: P(HIV | IVDU) = P(HIV | not IVDU)

H1: P(HIV | IVDU) > P(HIV | not IVDU)

HIV Seropositivity
POSITIVE	NEGATIVE
YES	312 276.20 ( 4.64)	27 62.80 ( 20.41)	339
NO	75 110.80 ( 11.57)	61 25.20 ( 50.88)	136
	387	88	475

χ² = 87.502,     df = 1,     χ²/df = 87.50 ,         P(χ² > 87.502) = 0.0000

critical Chi-square (Χ²) value= 6.634896

Since the P-value(0.000) is less than the significance level (0.05), we cannot accept the null hypothesis.

So the risk of HIV infection in this population of women is lower in non IV drug users

(c)

(i)

The risk of HIV infection who do not report a history of IVDU is 75/136 = 0.5515

the risk of HIV infection who report a history of IVDU is 312/339 = 0.9204

So, the estimated difference in risk is 0.9204 - 0.5515 = 0.3689

(ii)

The critical value for α=0.05 is 1.96.

(0.92-0.551-196-v0.92(339092)+ 0.551(1360.551) 0.92(1 - 0.92) 0.551(1 0.551) 0.92-0.551-1.96 × = 339 136 (0.28,0.457) =

we are 95% confident that the true difference between population proportions is contained by the interval (0.28, 0.457).

(iii)

This suggests a relatively high prevalence of HIV among incarcerated women that do not report IV drug use (55%), and a statistically significant increase in seropositivity among the women that do report IV drug use(92%)