1. Suppose we want to test the null hypothesis that p = 0.5 against the alternative p = 0.2, where p is the probability that a coin will land heads. Let
Y denote the number of heads in n independent tosses of the coin. Calculate
(i) the probability of type I error, (ii) the probability of type II error, and
(iii) the power of the test procedure if
(a) n = 10 and the test procedure used is to reject the null hypothesis iff
Y ≤ 1;
(b) n = 100 and test procedure rejects the null hypothesis iff Y ≤ 10