Answer
$F_0\gt F_{\frac{α}{2},n_1-1,n_2-1}$: null hypothesis is rejected.
There is enough evidence to conclude that the standard deviation time to earn a bachelor’s degree is different between the two groups.
Work Step by Step
$H_0:~σ_1=σ_2$ versus $H_1:σ_1\neσ_2$
$F_0=\frac{s_1^2}{s_2^2}=\frac{1.162^2}{1.015^2}=1.31$
$d.f_1=n_1-1=268-1=267$
$d.f_2=n_2-1=1145-1=1144$
Two-tailed test:
$F_{\frac{α}{2},n_1-1,n_2-1}=F_{0.025,267,1144}=1.29$
(According to table VIII, for $d.f._1=120$, the closest value to 267, $d.f._2=1000$, the closest value to 1144, and area in the right tail = 0.025)
$F_{1-\frac{α}{2},n_1-1,n_2-1}=F_{0.975,267,1144}=\frac{1}{F_{0.025,267,1144}}=\frac{1}{1.29}=0.78$
Since $F_0\gt F_{\frac{α}{2},n_1-1,n_2-1}$, we reject the null hypothesis.
