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Abstract Consider the problem of testing the hypothesis H 0: θ ∈ W 0 against the alternative H 1: θ ∈ W 1 when a certain subset E 0 ⊂ W 1 is given. This subset E 0 is such that the risk of accepting H 0 will be significant economically only if θ ∈ E 0. For this problem a test obtained by generalising the equal probability test of Arrow (1960) is suggested. Applications of the test procedure to the problems of combining several independent tests and of comparing several populations with a standard are discussed.
Umesh D. Naik (Mon,) studied this question.
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