1. In a clinical trial to study the effectiveness of a new pain reliever, a sample of 250 patients was given the new drug, and an independent sample of 100 patients was given a placebo. Of the patients given the new drug, 186 reported substantial relief, and of the patients given the placebo, 56 reported substantial relief. Find a 99% confidence interval for the difference between the proportions of patients experiencing substantial relief.
2. Two extrusion machines that manufacture steel rods are being compared. In a sample of 1000 rods taken from machine 1, 960 met specifications regarding length and diameter. In a sample of 600 rods taken from machine 2, 582 met the specifications. Machine 2 is more expensive to run, so it is decided that machine 1 will be used unless it can be convincingly shown that machine 2 produces a larger proportion of rods meeting specifications.
a. State the appropriate null and alternate hypotheses for making the decision as to which machine to use.
b. Compute the P-value.
c. Which machine should be used?