1. [MODULE 12] A total of 800 subjects were recruited into a clinical trial designed to test the efficacy of a new vaccine for the treatment of influenza. Half the subjects were assigned to the vaccine treatment, while the remaining half were assigned to the placebo. The following contingency table gives the frequencies of subjects who had flu, and those that did not have flu within one year of treatment: Response Treatment No Flu Flu Vaccine 202 198 Placebo 179 221 (a) For each treatment: i. Estimate the population proportion of subjects catching the flu. ii. Compute the standard error of the estimated population pro- portions. iii. Compute a 95% confidence interval for the population pro- portion for each group. (b) Test the null hypothesis that the population proportion for the vaccine group is equal to the population proportion for the placebo group at the a = 0.05 level. i. Give the standard error of the difference in sample propor- tions. ii. Give your test statistic. iii. What are your conclusions? (c) Compute the 95% confidence interval for the difference in popula- tion proportions between the placebo and vaccine groups. What is your interpretation of this confidence interval