2. The following table summarizes the information from a randomized clinical trial that compared two treatments (test and placebo) for a respiratory disorder. Respiratory Outcomes Treatment Favorable Unfa-orable Total Placebo 17 48 65 Test 40 20 60 Use formula to do (a)(c) and (f) manually (you'll need software to get critical value or pvalue). (a) (4 pts) Estimate the proportion of favorable responses using the test treatment and construct a 95% CI for it. (b) (5 pts) Estimate the proportion of favorable responses using the placebo treatment and test whether the true probability equal to 0.5 at oz = 0.05. Specify your hypothesis, the test statistics and its distribution, rejection region or pvalue, and draw your conclusion. (0) (5 pts) Construct a 90% condence interval for the difference of proportions of favorable opinions in the two groups. Based on the CI, is there an association between treatment and response? If there is association, how are they associated? (d) (7 pts) Use software to redo (a)(c). Provide your code, necessary output, and clearly label your results. (e) (6 pts) Estimate the odds ratio and then use software to construct a 90% condence interval for it. Can we get the same conclusion as in part (c)? (f) (8 pts) Use formula to conduct a test of statistical independence using Pearson's chisquare test and likelihood ratio test. For each test, specify your hypothesis, the test statistics and its distribution, rejection region or pvalue, and draw your conclusion