CAS Exam MAS-I Fall 2018, Question 21
Study guide: Exam MAS-I
Two independent populations X and Y have the following density functions:
f(x) = \lambda x^{\lambda-1}for0 < x < 1g(y) = \mu y^{\mu-1}for0 < y < 1
X_1, X_2, \ldots, X_n and Y_1, Y_2, \ldots, Y_m are random samples of sizes n and m, from X and Y, respectively.
You want to perform the following hypothesis test:
H_0: \lambda = 2;\ \mu = 4H_1: \lambda = 3;\ \mu = 8
Determine the form of the best critical region for this test, using the Neyman-Pearson lemma.
- A)
\sum_{i=1}^{n} \ln X_i + 4\sum_{i=1}^{m} \ln Y_i \le c - B)
\sum_{i=1}^{n} \ln X_i + 4\sum_{i=1}^{m} \ln Y_i \ge c - C)
4\sum_{i=1}^{n} \ln X_i - \sum_{i=1}^{m} \ln Y_i \le c - D)
4\sum_{i=1}^{n} \ln X_i - \sum_{i=1}^{m} \ln Y_i \ge c - E) The answer is not given by (A), (B), (C), or (D)
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