6.5.3(b) Lex X1,…Xn and Y1,..Ym are independent random samples from N( θ1, θ3) and
N( θ2, θ4), respectively. Show that the likelihood ratio test for testing H0: θ3= θ4, θ1 and θ2 unspecified, against H1: θ3 ^= θ4, θ1 and θ2 unspecified, can be based on the random variable
F= Sum from 1 to n (Xi-Xbar)^2/(n-1)
Sum from 1 to m (Yi-Ybar)^2/(m-1).
The solution uses proof and a step-by-step equation to answer the question in an attachment.