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 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. 240 women 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-six of the 120 women treated with Nevaripine experienced virologic failure, while 10 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. Virologic Failure
Yes No Total
Nevarpine 26 24 120
Lopinavir 10 110 120
Total 36 204 240

Required:
a. State appropriate hypotheses to test for association of treatment and virologic failure.
b. 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.