# Hypotheses Testing-Uniformly Most Powerful Test (ISS (Statistical Services) 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

### Describe in Detail

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

### Explanation

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 if