A researcher wants to determine if two alternative drugs have a differential effect on the pain symptoms of a specific rare disease. From hospitals across the country a random sample of patients with the disease is drawn. Roughly half is randomly assigned to drug A and the other to drug B. Three hours after the drug administration, each patient is asked to rate the amount of pain reduction as a percentage figure. The results are given below: Drug A n1 49, x1 = 27, $7 = 81 Drug B n2-52, x2 = 31, $2 = 144 Conduct a test to evaluate if there is enough evidence to claim that the average level of pain reduction is different for drug A and B. (a) (3 points) Write down the null and alternative hypotheses and explain what you are testing. Is the alternative hypothesis one-sided or two-sided? (b) (4 points) Compute the two-sample t-statistic. (c) (2 points) Estimate the degrees of freedom for the two-sample t-statistic. (d) (4 points) Find the P-value from the t distribution in Table C. State your decision rule regarding the hypotheses with an alpha level of .05. Interpret your results. Is there enough evidence to claim that the average level of pain reduction is different for both drugs? (e) (4 points) Estimate a 95% confidence interval and interpret your results