Theorem 18-3. If A is the likelihood tatio for testing a simple hypothesis Ho and if U = O(2) is a monotonic increasing (decreasing) function of 1 then the test based on U is equivalent to the...

Prove the theorem

Extracted text: Theorem 18-3. If A is the likelihood tatio for testing a simple hypothesis Ho and if U = O(2) is a monotonic increasing (decreasing) function of 1 then the test based on U is equivalent to the likelihood ratio test. The critical region for the test based on U is : $(0) < u="">< ¢(^o),="" f="" [ø(^o)="">< u=""><>