Difference in proportions A clinical trial is performed to evaluate the effectiveness of a new asthma medication. A simple random sample is taken of 1,000 patients with asthma. Of these,

700 are placed at random in the experimental group (Group 1), while the remaining 300 are placed in the control group (Group 2). The experimental group is given the new medication once a day for six months. The control group is given a placebo once a day for six months. After six months, 354 of the experimental group and136 of the control group have seen a reduction in the severity of their asthma symptoms. (i) Let p1 denote the true proportion of all asthma patients who would see a reduction in symptoms after six months of taking the new drug, and let p2 denote the true proportion of all asthma patients who would see a reduction in symptoms after six months of taking a placebo. Construct a 95% confidence interval for the difference pi – P2. Does your confidence interval contain 0? (ii) Compute the attained significance level for a one-sided hypothesis test with null hypothesis Ho : P1 – p2 = 0 and alternative hypothesis Ha : P1 – P2 > 0. (iii) Would the medication be considered better than a placebo at the a = 0.10significance level? What about at the a = 0.05 significance level? (iv) When publishing their findings, the researchers use a signficant level of a = 0.10 to conclude that “the medication is effective at treating asthma symptoms." Explain why that claim, though statistically justified, is subjective.