In Relief from Arthritis published by Thorsons Publishers, Ltd., John E. Croft claims that over 40% of those who suffer from osteoarthritis receive measurable relief from an ingredient produced by a particular species of mussel found off the coast of New Zealand. To test this claim, the mussel extract is to be given to a group of 7 osteoarthritic patients. If 3 or more of the patients receive relief, we shall not reject the null hypothesis that p = 0.4; otherwise, we shall conclude that p < 0.4.

(a) Evaluate α, assuming that p = 0.4.

(b) Evaluate β for the alternative p = 0.3.