Question

For the likelihood ratio statistic of Exercise 12.22, show that –2 ∙ ln λ approaches t2 as n → ∞.
In exercise
A random sample of size n from a normal population with unknown mean and variance is to be used to test the null hypothesis µ = µ0 against the alternative µ ≠ µ0. Using the simultaneous maximum likelihood estimates of µ and σ2 obtained in Example 10.18 on page 300, show that the values of the likelihood ratio statistic can be writ-ten in the form
Where t =  – µ0 / s/√n. The likelihood ratio test can thus be based on the t distribution.


$1.99
Sales0
Views25
Comments0
  • CreatedNovember 04, 2015
  • Files Included
Post your question
5000