Answer
$F_0\gt F_{1-α,n_1-1,n_2-1}$: null hypothesis is not rejected.
There is not enough evidence to conclude that $σ_1\ltσ_2$
Work Step by Step
$H_0:~σ_1=σ_2$ versus $H_1:σ_1\ltσ_2$
$F_0=\frac{s_1^2}{s_2^2}=\frac{8.4^2}{10.3^2}=0.67$
$d.f_1=n_1-1=45-1=44$
$d.f_2=n_2-1=41-1=40$
Left-tailed test:
$F_{α,n_1-1,n_2-1}=F_{0.01,44,40}=2.01$
(According to table VIII, for $d.f._1=40$, the closest value to 44, $d.f._2=50$, the closest value to 40, and area in the right tail = 0.01)
$F_{1-α,n_1-1,n_2-1}=F_{0.99,44,40}=\frac{1}{F_{0.01,44,40}}=\frac{1}{2.01}=0.50$
Since $F_0\gt F_{1-α,n_1-1,n_2-1}$, we do not reject the null hypothesis.
