2. Suppose that in a hypothetical study on the effects of azidothymidine (AZT) in slowing the development of AIDS symptoms, 488 veterans whose immune systems were beginning to falter after infection with the HIV virus were randomly assigned either to receive AZT immediately or to wait until their T cells showed severe immune weakness. The study recorded how many subjects developed AIDS symptoms by the end of the trial period in every group dened by age, race and AZT use. Age Race AZT AIDS Yes No older white yes 2 28 no 5 38 black yes 5 42 no 8 22 younger white yes 14 93 no 32 81 black yes 11 52 no 12 43 (a) Write the logistic model for the probability of AIDS development as a function of race, age, use of AZT. Be mindful of the categories of the covariates, and use the notation of the regression parameters, such 30, 31 etc. Your model should not contain any interaction term of the covariates. [5] (b) Fit the model to the data, and estimate the odds ratio of AIDs development from AZT use to no AZT use, and interpret the result. More specically, you are asked to estimate the conditional odds ratio given age and race. [5] (c) Calculate the 95% condence interval for the above odds ratio. DO NOT provide the condence interval for the log-odds ratio. [5] ((1) Conduct a hypothesis test if early use of AZT reduces the chance of the development of AIDS symptoms for any given age and race group. Make sure to state the hypothesis correctly, report the test statistic and p-value, and write the conclusion. [5] (e) Check if age and race have any effect on the AIDS development for the underlying population. Do not conduct the test for age effect and race effect separately. Make sure to state the hypothesis correctly in terms of the parameters used in dening the logistic model in part (a), report the test statistic and p-value, and write the conclusion. [5] (f) Obtain the standardized residuals, and check if any data points show lack-of-t. Also, carry out the lack-of-t test using the residual deviance statistic. [5]