A dry cleaning establishment claims that a new spot remover will remove more than 70% of the spots to which it is applied. To check this claim, the spot remover will be used on 12 spots chosen at random. If fewer than 11 of the spots are removed, we shall not reject the null hypothesis that p = 0.7: otherwise, we conclude that p > 0.7.

(a) Evaluate a, assuming that p = 0.7.

(b) Evaluate 8 for the alternative p = 0.9.