Solution Found!
Suppose that Y1, Y2, . . . , Yn are independent, normally
Chapter 11, Problem 28E(choose chapter or problem)
Problem 28E
Suppose that Y1, Y2, . . . , Yn are independent, normally distributed random variables with E(Yi) = β0 + β1 xi and V (Yi ) = σ 2, for i = 1, 2, . . . , n. Show that the likelihood ratio test of H0 : β1 = 0 versus Ha : β1 ≠ 0 is equivalent to the t test given in this section.
Questions & Answers
QUESTION:
Problem 28E
Suppose that Y1, Y2, . . . , Yn are independent, normally distributed random variables with E(Yi) = β0 + β1 xi and V (Yi ) = σ 2, for i = 1, 2, . . . , n. Show that the likelihood ratio test of H0 : β1 = 0 versus Ha : β1 ≠ 0 is equivalent to the t test given in this section.
ANSWER:
Step 1 of 10
The density function of the random variable
where
Because the random variables are independent, the likelihood function is equal to: