Let X1,X2, . . . ,Xn be a random sample from an
Chapter 8, Problem 8E(choose chapter or problem)
Let \(X_{1}, X_{2}, \ldots, X_{n}\) be a random sample from an exponential distribution with mean \(\theta\). Show that the likelihood ratio test of \(H_{0}: \theta=\theta_{0}\) against \(H_{1}: \theta \neq \theta_{0}\) has a critical region of the form \(\sum_{i=1}^{n} x_{i} \leq c_{1}\) or \(\sum_{i=1}^{n} x_{i} \geq c_{2}\). How would you modify this test so that chi-square tables can be used easily?
Equation Transcription:
Text Transcription:
X_1,X_2,,X_n
theta
H_0:theta =theta_0
H_1:theta not =theta_0
sum_i=1^n x_i < or =c_1
sum_i=1^n x_i> or = c_2
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