The article “HIV-positive Smokers Considering Quitting: Differences by Race/Ethnicity” (E. Lloyd- Richardson, C. Stanton, et al., Am J Health Behav, 2008:3–15) surveyed 444 HIV-positive smokers. Of these, 170 reported that they had used a nicotine patch. Consider this to be a simple random sample.

a. Find a 95% confidence interval for the proportion of HIV-positive smokers who have used a nicotine patch.

b. Find a 99% confidence interval for the proportion of HIV-positive smokers who have used a nicotine patch.

c. Someone claims that the proportion is less than 0.40. With what level of confidence can this statement be made?

d. Find the sample size needed for a 95% confidence interval to specify the proportion to within ± 0.03.

e. Find the sample size needed for a 99% confidence interval to specify the proportion to within ± 0.03.