5.17 A random sample of 180 men who took the driving test found that 103 passed. A similar sample of 225 women found that 105 passed. Test whether pass rates are the same for men and women. 5.18

(a) A pharmaceutical company testing a new type of pain reliever administered the drug to 30 volunteers experiencing pain. Sixteen of them said that it eased their pain. Does this evidence support the claim that the drug is effective in combating pain?

(b) A second group of 40 volunteers were given a placebo instead of the drug. Thirteen of them reported a reduction in pain. Does this new evidence cast doubt upon your previous conclusion? 5.19

(a) A random sample of 20 observations yielded a mean of 40 and standard deviation 10. Test the hypothesis that μ = 45 against the alternative that it is not. Use the 5% significance level.

(b) What assumption are you implicitly making in carrying out this test?