Answer
$F_0\lt F_{1-α,n_1-1,n_2-1}$: null hypothesis is not rejected.
There is not enough evidence to conclude that students who do not plan to apply for financial aid have a higher standard deviation on the SAT I math exam than students who plan to apply for financial aid.
Work Step by Step
$s_1,n_1~and~d.f._1$ refer to the "do not plan" group and $s_2,n_2~and~d.f._2$ refer to the "plan" group.
$H_0:~σ_1=σ_2$ versus $H_1:σ_1\gtσ_2$
$F_0=\frac{s_1^2}{s_2^2}=\frac{123.1^2}{119.4^2}=1.06$
$d.f_1=n_1-1=35-1=34$
$d.f_2=n_2-1=38-1=37$
Right-tailed test:
$F_{α,n_1-1,n_2-1}=F_{0.01,34,37}=2.54$
(According to table VIII, for $d.f._1=30$, the closest value to 34, $d.f._2=25$, the closest value to 37, and area in the right tail = 0.01)
Since $F_0\lt F_{1-α,n_1-1,n_2-1}$, we do not reject the null hypothesis.
