Question

A 2007 study of women in Miami (Brewer et al., Ann Epidemiol. 17:533-539) examined the link between HIV status and high-risk sexual activity. Eligible participants were female, at least 18 years of age, English-speaking, self-reported having vaginal or anal sex in the past 30 days, and self-reported having smoked crack or snorted or injected cocaine or heroin in the last 30 days and having not been in drug treatment in the last 30 days. The data set HIVrisk.dta contains two columns: risk for unprotected sex and HIV for HIV status. Each woman knew her HIV status.

d. (2) What proportion of the HIV-negative group engaged in unprotected sex? Provide a 95% CI for the true proportion. _____________; ________________________

e. (2) Test the null hypothesis that the proportion of HIV-positive women having unprotected sex is equal to the proportion of HIV-negative women having unprotected sex (group proportion comparison). Provide the p-value and state the conclusion.

HIV	risk
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	yes
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Negative	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	no
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes
Positive	yes

Answer 1

HIV- Positive women:

Total HIV positive women, n = 117

Have unprotected sex = 88

Does not have unprotected sex = 29

HIV- Negative women:

Total HIV negative women, n = 61

Have unprotected sex = 34

Does not have unprotected sex = 27

d) Proportion of HIV-negative group engaged in unprotected sex = 34/ 61 = 0.557

95% Confidence Interval for the true proportion

At =0.05,

e) Proportion of HIV-positive group engaged in unprotected sex = 88/ 117 = 0.752

Proportion of HIV-negative group engaged in unprotected sex = 34/ 61 = 0.557

Pooled proportion, = (88 + 34)/ (117+61)} = 0.685

Null and Alternative Hypotheses

Test Statistics:

P-value approach:

p = 0.0079

If p=0.0079 > , then do not reject the null hypothesis.

if p=0.0079 < , then reject the null hypothesis.