Problem 3 (Exercise 10 on p.591 of DeGroot and Schervish) Lyle et al. (1987) ran an experiment to study the effect of a calcium supplement on blood pressure. A group of 10 subjects received a calcium supplement, and another group of 11 subjects received a placebo. The experiment lasted 12 weeks. Both before and after the 12-week period, each participant had systolic blood pressure measured while at rest. The changes (after minus before) are given in the following table:
Calcium 7 -4 18 17 -3 -5 1 10 11 -2
Placebo -1 12 -1 -3 3 -5 5 2 -11 -1 -3
Test the null hypothesis that the mean change in blood pressure for the calcium supplement group is lower than the mean change in blood pressure for the placebo group. Use significance level $\alpha = 0.1$.