In July 2008 the US National Institutes of Health announced that it was stopping a clinical study early because of unexpected results. The study population consisted of HIV-infected women in sub-Saharan Africa who had been given single dose of Nevaripine (a treatment for HIV) while giving birth, to prevent transmission of HIV to the infant. The study was a randomized comparison of continued treatment of a woman (after successful childbirth) with Nevaripine vs. Lopinavir, a second drug used to treat HIV. There were 240 women who participated in the study; 120 were randomized to each of the two treatments. Twenty-four weeks after starting the study treatment, each woman was tested to determine if the HIV infection was becoming worse (an outcome called virologic failure). Twenty-eight of the 120 women treated with Nevaripine experienced virologic failure, while 12 of the 120 women treated with the other drug experienced virologic failure. A two- way table presenting the results of this study is given below. (10 points total) Virologic Failure Yes No Total Nevaripine 28 92 120 Treatment Lopinavir 12 108 120 Total 40 200 240 (1) State appropriate hypotheses to test for association of treatment and virologic failure. (2) Complete the hypothesis test with the Chi-square test and state an appropriate conclusion. Do the test manually, calculating all of the expected values, the Chi-square statistic, and use R to find the p-value. Use the 5% significance level for the hypothesis test