Hypotheses Testing-Uniformly Most Powerful Test (ISS Statistics Paper II (Old Subjective Pattern)): Questions 1 - 1 of 1

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Question number: 1

» Hypotheses Testing » Uniformly Most Powerful Test

Appeared in Year: 2015

Essay Question▾

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Fins a Most powerful test for testing the simple hypothesis Equation against the simple alternative hypothesis Equation based on n random observations from N (µ, σ 2) where µ is know. Show that this MP test is UMP (Uniformly most powerful).


Let X i ’s are n random observations from N (µ, σ 2) and the pdf is


The hypothesis is


To find the most powerful test, we use following step


The N-P test is


Given α, we can find k by solving Equation if

Equation<span class="more">… (59 more words) …</span>

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