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. Proportion of the Population Sample Sample Sample active ingredients size variance 15% 10.75 40% 35 14.08 50% 25 15.02 8.65 mean mean 23.45 30 9.62 12 43 For your convenience, the within-sample variation is sx = 9.729.Consider the contrasts below: 16241 - 42 - 43 by M2 - M3 (a) (10 points) Construct a 95% two-sided confidence interval for ly. (b) (10 points) Construct a 95% two-sided confidence interval for lz. c) (10 points) Using the Bonferroni correction, construct 95% simultaneous two-sided confidence intervals for, and 12