Question:
A test which maximizes the power of the test for fixed size \(\alpha\) is called as :
A test which maximizes the power of the test for fixed size \(\alpha\) is called as :
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Think of the general name given to Most Powerful / Uniformly Most Powerful tests in hypothesis testing theory, not the construction method.
Updated On: Jul 4, 2026
- Bayes test
- Likelihood ratio test
- Randomized test
- Optimal test
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The Correct Option is D
Solution and Explanation
Step 1: In the theory of testing hypotheses, several types of tests are defined. A Bayes test minimizes the Bayes risk using a prior distribution on the parameter space. A likelihood ratio test is a general method of constructing a test using the ratio of likelihoods under the null and alternative hypotheses. A randomized test introduces an extra randomization device at the boundary of the critical region so that an exact size \(\alpha\) can be achieved, typically for discrete distributions.
Step 2: A test that is constructed specifically to maximize the power (the probability of correctly rejecting a false null hypothesis) among all tests of a given fixed size \(\alpha\) is what the theory calls an optimal (optimum) test, covering Most Powerful and Uniformly Most Powerful tests studied under this heading.
Step 3: Bayes tests do not fix \(\alpha\) and instead minimize overall risk, likelihood ratio tests are a construction tool (which happens to produce the optimal test in the simple-vs-simple case, per Neyman-Pearson), and randomized tests are a device to fix the size exactly, not to define power-maximization. The description in the question matches the definition of an optimal test.
Final Answer: \[\boxed{\text{Optimal test}}\], option (D).
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