Binomial distribution test We have X1, ...; Xn, a random sample of size n from a Bernoulli distribution with the parameter p. We are interested in a hypotheses test with . Ho : p = 1/3 . H1 : p > 1/3. 1. Suppose n = 10. Consider C = {X, : _ X, 2 6). What is the significance level of this test? Hint: You may find the R outcome of pbinom (0:10, 10, 1/3) useful. 2. Suppose n = 10. Consider C = {X; : _ X; 2 6). What is the power of this test when true p is 1/2? Hint: You may find the R outcome of pbinom (0:10, 10, 1/2) useful. 3. Now n = 100. a. If we use C = {X, : EX; 2 41}, what is the significance level of this test? Hint: pbinom (41, 100, 1/3) is useful. b. With CLT we have that Vn (p - p) -+d N(0, p(1 - p)). Observe that he C = {X, : _ X; 2 41} in part a is same as C = {X, : p 2 0.41}. Using CLT, find an approximate significance level of this test