Which of the following statements are needed in constructing the likelihood ratio test?
A) Finding the largest value of the likelihood for any $\theta \text { in } \Omega _ { 0 }$
(by finding the maximum
Likelihood estimate within $\Omega _ { 0 }$
And substituting back into the likelihood function).
B) Find the largest value of the likelihood for any $\theta \text { in } \Omega _ { \mathrm { 0 } }$
C) Forming the ratio $\lambda \left( x _ { 1 } , \ldots , \ldots , x _ { n } \right)$
= maximum likelihood for $\theta \text { in } \Omega _ { 0 } /$
Maximum likelihood for $\theta \text { in } \Omega _ { \mathrm { 0 } }$
D) All of the above statements are needed.
E) Only statements A and B are needed.

Question

Which of the following statements are needed in constructing the likelihood ratio test?
A) Finding the largest value of the likelihood for any $\theta \text { in } \Omega _ { 0 }$
(by finding the maximum
Likelihood estimate within $\Omega _ { 0 }$
And substituting back into the likelihood function).
B) Find the largest value of the likelihood for any $\theta \text { in } \Omega _ { \mathrm { 0 } }$ 
C) Forming the ratio $\lambda \left( x _ { 1 } , \ldots , \ldots , x _ { n } \right)$
= maximum likelihood for $\theta \text { in } \Omega _ { 0 } /$
Maximum likelihood for $\theta \text { in } \Omega _ { \mathrm { 0 } }$ 
D) All of the above statements are needed.
E) Only statements A and B are needed.

Quizplus · Accepted Answer

The likelihood ratio test involves finding the maximum likelihood estimates under both the null and alternative hypotheses and forming their ratio. Thus, all the statements A, B, and C describe necessary steps in constructing the likelihood ratio test, making D the correct choice.

Which of the Following Statements Are Needed in Constructing the Likelihood