# Hypotheses Testing-Likelihood Ratio Test (ISS Statistics Paper II (Old Subjective Pattern)): Questions 1 - 2 of 2

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## Question number: 1

» Hypotheses Testing » Likelihood Ratio Test » ASN Function

Appeared in Year: 2015

Essay Question▾

### Describe in Detail

Derive the likelihood ratio test for comparing the means of k independent homoscedastic normal populations.

### Explanation

Given that there are k independent homoscedastic normal populations that is the variance is same i. e. ; i = 1, 2, …, k. We have to test

In the X population the sample is = { (x i1, x i2, …, x ini)

The… (75 more words) …

## Question number: 2

» Hypotheses Testing » Likelihood Ratio Test » ASN Function

Appeared in Year: 2014

Essay Question▾

### Describe in Detail

x 1 , x 2 , …, x n is a random sample from N (θ, σ 2 ) (σ 2 not specified). Derive likelihood ratio test of testing H 0 : θ=θ 0 against H 1 : θ ≠ θ 0 .

### Explanation

Under the given model, the parameter space is

Under H 0 , the parameter space is

The likelihood function is

Under the whole space, the unrestricted MLE is

Under H 0 , the restricted MLE is

The statistic is

The likelihood… (63 more words) …

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