CAS Exam MAS-I Spring 2018, Question 19
Study guide: Exam MAS-I
Let X_1, \ldots, X_n be a random sample from a distribution with density function f(x) = \dfrac{2\theta^2}{(x+\theta)^3}, where n is large. You wish to test the hypothesis H_0: \theta = 1 against the hypothesis H_1: \theta \ne 1.
You perform this test, and the null hypothesis is rejected at a 1% significance using the Chi-squared approximation for the likelihood ratio test. Let \Lambda be the likelihood ratio for this hypothesis test.
Calculate the maximum possible value of \Lambda.
- A) Less than 0.01
- B) At least 0.01, but less than 0.02
- C) At least 0.02, but less than 0.03
- D) At least 0.03, but less than 0.04
- E) At least 0.04
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