Question

In: Statistics and Probability

Let X1, X2, … , X8 be a random sample of size 8 from a distribution with probability density function

where x ≥ 1. What is the likelihood ratio critical region for testing the null hypothesis ??: ? = 1 against ?1: ? ≠ 1? If ? = 0.1, determine the best likelihood ratio critical region?

Expert Solution

Answer:

Given that,

Let X1, X2, … , X8 be a random sample of size 8 from a distribution with probability density function,

where ? ≥ 1.

What is the likelihood ratio critical region for testing the null hypothesis ??: ? = 1 against ?1: ? ≠ 1? If ? = 0.1, determine the best likelihood ratio critical region:

For testing hypothesis:

Vs

=0.1

Now,

The likelihood function of sample is,

Now, n=8

Now,

We know that,

Therefore,

i.e,

We reject H_0 for smaller values of .

We reject H_0 for

Now,

The test function is,

orchestra answered 3 years ago

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Question

Let X1, X2, … , X8 be a random sample of size 8 from a distribution with probability density function

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