Question 4: Suppose that we have two independent binomial experiments of size n, and n2, respectively. The sample proportions are respectively #1 and 72, respectively. (a) Use the delta method to show that the estimated variance for the log relative risk can be computed as follows: V [log(71/ 712)] = 1 - 71 1 - 712 + n1 71 n2 712 Hint: Find a function T such that log(RR) - 7(#1, 72), and use the following linear approximation T(1, 12) ~ T(71, 72) + (OT/am1) (#1 - 71) + (OT/272) (12 - 712). (b) Consider an experiment with 71 = 0.0171 and 72 = 0.0094, n1 = 11034, n2 = 11037. Give a 95% confidence interval for the relative risk 71/72. (c) Consider the statistics from (b). Give the 95% Agresti-Caffo confidence interval for 71 - 72? (d) Consider the statistics from (b). Why do think the researchers of this study would prefer to compare m1 and 72 as a ratio instead of a difference