6.15 A researcher is interested in learning if a new drug is better than a placebo in treating a certain disease. Because of the nature of the disease, only a limited number of patients can be found. Out of these, five are randomly assigned to the placebo and five to the new drug.

Suppose that the concentration of a certain chemical in blood is measured and smaller measurements are better and the data are:

Drug: 3.2, 2.1, 2.3, 1.2, 1.5 Placebo: 3.4, 3.5, 4.1, 1.7, 2.1

(a) For the median test and the control median test, give the null hypothesis, the alternative hypothesis, the value of the test statistic, the exact and the approximate P value and a conclusion. What assumptions are we making?

(b) Use the median test to calculate a confidence interval for the difference between the medians. What is the largest possible level of confidence? What assumptions are we making for this procedure?