2. A pharmaceutical company is interested in the effectiveness of a new preparation designed to relieve arthritis pain. Three variations have been prepared for investigation, which differ according to the proportion of the active ingredients. Patients enrolled in the study are randomly assigned to one of the three-variations, and the time (in minutes) until pain relief is recorded on each subject. A summary of the study is given below. Population Sample Sample Sample Proportion of the active ingredients mean size mean variance 15% 141 30 23.45 10.75 40% 142 35 14.08 9.62 50% 143 25 15.02 8.65 For your convenience, the within-sample variation is sy = 9.729.Consider the contrasts below: 1211-12-13 l=112-113 (a) (10 points) Construct a 95% two-sided confidence interval for . (b) (10 points) Construct a 95% two-sided confidence interval for . (c) (10 points) Using the Bonferroni correction, construct 95% simultaneous two-sided confidence intervals for and .