Question

Two random variables A and B follow the normal distribution. Take 10 samples from each random variable and obtained standard variance s_A^2= 5, and s_B^2= 2. Use a significance level of 0.05, test the hypothesis that H0: sigma_1^2 / sigma_2^2 = 1 against the alternative H1: sigma_1^2 / sigma_2^2> 1

Answer 1

The null and alternate hypothesis are:

H0:

Ha:

The test statistic is given by:

Since this is a right-tailed test, so the critical-value is given by:

Since the test statistic value lies to the left of the critical value, so we do not have sufficient evidence to reject H0.

Thus, we cannot conclude that .