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Uniformly most powerful test hypothesis lies on both sides of the alternative). The reason is that in these situations, the most powerful test of a given size for one possible value of the parameter (e.g. for formula_48 where formula_49) is different from the most powerful test of the same size for a different value of the parameter (e.g. for formula_50 where formula_51). As a result, no test is uniformly most powerful in these situations. Uniformly most powerful test In statistical hypothesis testing, a uniformly most powerful (UMP) test is a hypothesis test which has the greatest power formula_1 among all possible tests of a