For the likelihood ratio statistic of Exercise 12.22, show that 2 ln λ approaches t2 as n
Question:
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 Ï2 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.
Transcribed Image Text:
-n/2 A =1+ n -
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Use ln1 x 12 x 2 ...View the full answer
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Related Book For
John E Freunds Mathematical Statistics With Applications
ISBN: 9780134995373
8th Edition
Authors: Irwin Miller, Marylees Miller
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