# Hypotheses Testing (ISS (Statistical Services) Statistics Paper II (Old Subjective Pattern)): Questions 7 - 9 of 9

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## Question number: 7

» Hypotheses Testing » Most Powerful Test

Appeared in Year: 2014

Essay Question▾

### Describe in Detail

Let X be r. v. with pmf under H 0 and H 1 given below. Find M. P. test with α=0.03

 x 1 2 3 4 5 6 f 0 (x) 0.01 0.01 0.01 0.01 0.01 0.95 f 1 (x) 0.05 0.04 0.03 0.02 0.01 0.85

### Explanation

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## Question number: 8

» Hypotheses Testing » Unbiased Test

Appeared in Year: 2015

Essay Question▾

### Describe in Detail

Explain the notion of unbiasedness with regards to a test of a hypothesis. Examine the validity of the statement. A most powerful test is invariably unbiased.

### Explanation

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## Question number: 9

» Hypotheses Testing » Uniformly Most Powerful Test

Appeared in Year: 2015

Essay Question▾

### 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

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