Answer
$F_{1-\frac{α}{2},n_1-1,n_2-1}\lt F_0\lt F_{\frac{α}{2},n_1-1,n_2-1}$: null hypothesis is not rejected.
There is not enough evidence to conclude that $σ_1\neσ_2$
Work Step by Step
$H_0:~σ_1=σ_2$ versus $H_1:σ_1\neσ_2$
$F_0=\frac{s_1^2}{s_2^2}=\frac{4.5^2}{3.8^2}=1.40$
$d.f_1=n_1-1=13-1=12$
$d.f_2=n_2-1=8-1=7$
Two-tailed test:
$F_{\frac{α}{2},n_1-1,n_2-1}=F_{0.025,12,7}=4.76$
(According to table VIII, for $d.f._1=10$, the closest value to 12, $d.f._2=7$ and area in the right tail = 0.025)
$F_{1-\frac{α}{2},n_1-1,n_2-1}=F_{0.975,12,7}=\frac{1}{F_{0.025,12,7}}=\frac{1}{4.76}=0.21$
Since $F_{1-\frac{α}{2},n_1-1,n_2-1}\lt F_0\lt F_{\frac{α}{2},n_1-1,n_2-1}$, we do not reject the null hypothesis.
