In the remainder of this chapter, we shall consider special testing situations that arise very often in applied work. In each of these situations, there does not exist, for each...., a UMP level......test. We shall derive test in these situations that are based on a generalization of the likelihood ratio defined on page 464. However, in more advanced courses, it can be shown that the.....tests and.....tests derived in Sections 8.5,8.6, and 8.7 are all UMP among various classes of unbiased tests of their sizes