CAS Exam MAS-I Spring 2018, Question 22

You are given the following information about samples from two populations:

A random sample of size 8, $X_1 \ldots X_8$ , was drawn from a normal population with unknown mean $\mu_1$ and unknown variance $\sigma_1^2$ , with $s_1^2 = \dfrac{\sum(x_i - \bar{x})^2}{7}$ .
A random sample of size 10, $Y_1 \ldots Y_{10}$ , was drawn from a normal population with unknown mean $\mu_2$ and unknown variance $\sigma_2^2$ , with $s_2^2 = \dfrac{\sum(y_i - \bar{y})^2}{9}$ .

You want to test the null hypothesis $H_0: \sigma_1^2 = \sigma_2^2$ against the alternative hypothesis $H_1: \sigma_1^2 < \sigma_2^2$ at a 5% significance level by using the statistic $\dfrac{s_1^2}{s_2^2}$ .

Calculate the boundary of the best critical region for the test.

A) Less than 1.5
B) At least 1.5, but less than 3.0
C) At least 3.0, but less than 4.5
D) At least 4.5, but less than 6.0
E) At least 6.0

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CAS Exam MAS-I Spring 2018, Question 22

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