Question

2 pts Question 4 Consider the following hypothesis. H : 01 = 02 H: 01 02 Find the rejection region (step 2). Si 28, S2 = 17, nj = 8, n2 =5, a = 0.100. NOTE: Round your answer to TWO decimal places.

Answer 1

$\\Standard\; Deviation 1(S_1) = 28 \\Standard\; Deviation 2(S_2) = 17 \\Sample\;Size(n_1) = 8 \\Sample\;Size(n_2) = 5 \\\alpha = 0.1$

We are interested in testing the hypothesis
$\\Null\;Hypothesis --> H_0: \sigma_1 = \sigma_2 \\Alternate\;Hypothesis --> H_1: \sigma_1 \ne \sigma_2$

Assuming normality of the sampled populations, the F-static is

fo S2 S} 784.0 289.0 = 2.71

from the table of Percentage Points of the F-distribution, we find that
$\\f_{1-\alpha/2, n_1-1, n_2-1} = \\f_{0.95, 7, 4} = 0.24 \\f_{\alpha/2, n_1-1, n_2-1} = f_{0.05, 7, 4} = 6.09 \\\\\text{Decision Rule: Reject the null hypothesis if, }\\f_0 > f_{\alpha/2, n_1-1,n_2-2}\text{{ or }}f_0 < f_{1-\alpha/2, n_1-1,n_2-1}\\\text{; otherwise do not reject }H_0 \\\\\text{The rejection region is }f_0 > 6.09\text{ or }f_0 < 0.24$

CONCLUSION:
Since the test statistic value 2.71 is between 0.24 and 6.09, so we fail to reject the null hypothesis.