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▾

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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. Xi~N(μi,σ2); i = 1, 2, …, k. We have to test

H0:μ1=μ2==… (806 more words) …

Question number: 2

» Hypotheses Testing » Likelihood Ratio Test » ASN Function

Appeared in Year: 2014

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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

H=((θ,σ2);θR,σ2>0)

Under H 0 , the parameter space is

H0=((θ0,σ2);σ2>… (640 more words) …

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