Problem 1. Let X be a random vector with density fo for some 0 e O and o be a number in (0, 1). (1) Suppose * be a 1 - a confidence region. Show that the test which rejects the null hypothesis Ho : 0 = 60 when # does not contain do has size at most a. (2) Let o(X, do) be a test of Ho : 0 = do of size at most o for every do E O. Show that {60 E Oo : 6(X, 60) = 0} is a 1 - a confidence region