Let independent random samples of sizes n and m be taken
Chapter 8, Problem 9E(choose chapter or problem)
PROBLEM 9E
Let independent random samples of sizes n and m be taken respectively from two normal distributions with unknown means μX and μY and unknown variances σ2 X and σ2Y .
(a) Show that when σ2X= σ2Y , the likelihood ratio for testingH0: μX = μY against H1: μX ≠ μYis a function of the usual two-sample t statistic.
(b) Show that the likelihood ratio for testing H0: σ2X =σ2Y against H1: σ2X ≠ σ2Y is a function of the usual two-sample F statistic.
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