[Based on Koh, et al. (1997). Effects of hormone-replacement therapy on fibrinolysis in postmenopausal women. New England Journal of Medicine 336,683-690, which is the basis of Exercise 8.S.22.] Researchers wanted to test the effect of oral conjugated estrogen on plasminogen-activator inhibitor type 1 (PAI-1). They took measurements on each of 30 women before taking conjugated estrogen and after taking conjugated estrogen. They then prepared to analyze the data from this paired design. One researcher. Smith, wanted to conduct a sign test. Another, Jones, advocated a paired t test on the grounds that the sign test uses only part of the information in the data (namely, whether the before -after difference is positive or negative) and thus is less powerful than the t test.
(a) What did Jones mean in saying that the sign test "is less powerful than the t test"?
(b) Assuming that Jones is correct, why would anyone ever conduct a sign test?