For the likelihood ratio statistic of Exercise 12.22, show that 2 ln λ approaches t2 as n

For the likelihood ratio statistic of Exercise 12.22, show that €“2 ˆ™ ln λ approaches t2 as n †’ ˆž.
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/ˆšn. The likelihood ratio test can thus be based on the t distribution.

Transcribed Image Text:

-n/2 A =1+ n -