Chapter 8.6, Problem 8.78LM

Independent random samples were selected from each of two normally distributed populations, n₁ = 12 from population 1 and n₂ = 27 from population 2. The means and variances for the two samples are shown in the table.

Sample 1	Sample 2
n1 = 12	n2 = 27
${\bar{x}}_1=31.7$	${\bar{x}}_2=37.4$
$s_1^2=3.87$	$s_2^2=8.75$

1. a. Test the null hypothesis $H_{\text{0}}:{\sigma }_1^2={\sigma }_2^2$ against the alternative hypothesis $H_{\text{a}}:{\sigma }_1^2\ne {\sigma }_2^2$. Use α = .10.
2. b. Find and interpret the approximate p-value of the test.