# Question

A random sample of size n is to be used to test the null hypothesis that the parameter θ of an exponential population equals θ0 against the alternative that it does not equal θ0.

(a) Find an expression for the likelihood ratio statistic.

(b) Use the result of part (a) to show that the critical region of the likelihood ratio test can be written as

(a) Find an expression for the likelihood ratio statistic.

(b) Use the result of part (a) to show that the critical region of the likelihood ratio test can be written as

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