Question

Two random samples were independently generated from two populations, as follows below. The two populations share the same variance of σ². X can be considered the control group and Y the treatment group.

and   

A. Find the likelihood function, i.e., the joint density function of X and Y.

B. Derive the maximum likelihood estimates of μ1, μ2, and σ².

C. Suppose the null hypothesis is μ1=μ2 and alternative hypothesis is μ1 μ2. Write the formula for calculating the likelihood of the null hypothesis and the formula for calculating the likelihood of the alternative hypothesis.

D. How do you interpret the likelihood scores of the null and alternative hypotheses?

E. How do you perform the likelihood ratio test for the null and alternative hypotheses specified in (C)?

Answer 1