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 $σ_1\neσ_2$.
Work Step by Step
$H_0:~σ_1=σ_2$ versus $H_1:σ_1\neσ_2$
$F_0=\frac{s_1^2}{s_2^2}=\frac{18.3^2}{13.5^2}=1.84$
$d.f_1=n_1-1=61-1=60$
$d.f_2=n_2-1=57-1=56$
Two-tailed test:
$F_{\frac{α}{2},n_1-1,n_2-1}=F_{0.025,60,50}=1.72$
$F_{1-\frac{α}{2},n_1-1,n_2-1}=F_{0.975,60,56}=\frac{1}{F_{0.025,56,60}}=\frac{1}{\approx 1.75}=0.57$
Since $F_0\gt F_{\frac{α}{2},n_1-1,n_2-1}$, we reject the null hypothesis.
