It is suspected that a coin is not balanced (not fair). Let p be the probability of tossing a head. To test H0: p = 0.5 against the alternative hypothesis Ha: p > 0.5, a coin is tossed 15 times. Let Y equal the number of times a head is observed in the 15 tosses of this coin. Assume the rejection region to be {Y ≥ 10}.
(a) Find α.
(b) Find β for p = 0.7.
(c) Find β for p = 0.6.
(d) Find the rejection region for {Y ≥ K} for a = 0.01, and α = 0.03.
(e) For the alternative Ha: p = 0.7, find β for the values of α given in (d).