Math 6010 • Linear Models

Let \(X_1,X_2,\ldots,X_n\) be independent random variables. We assume that \(X_i\) has a Poisson\((\lambda_i)\) distribution. We wish to test
\[
H_0:\lambda_1=\lambda_2=\cdots=\lambda_n
\]
against the alternative
\[
H_A:H_0\text{ is not true.}
\]
\begin{enumerate}
\item Show that the likelihood ratio test and the \(\chi^2\) tests are equivalent under \(H_0\). (15 points)
\item Explain why and how the normal as well as the \(\chi^2\) distributions can be used to approximate the critical values. (5 points)
\end{enumerate}