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 $σ_1\gtσ_2$
Work Step by Step
$H_0:~σ_1=σ_2$ versus $H_1:σ_1\gtσ_2$
$F_0=\frac{s_1^2}{s_2^2}=\frac{7.5^2}{5.1^2}=2.16$
$d.f_1=n_1-1=23-1=22$
$d.f_2=n_2-1=13-1=12$
Right-tailed test:
$F_{α,n_1-1,n_2-1}=F_{0.05,22,12}=2.54$
Since $F_0\lt F_{1-α,n_1-1,n_2-1}$, we do not reject the null hypothesis.
