Answer
$F_0\gt F_{α,n_1-1,n_2-1}$: null hypothesis is rejected.
There is enough evidence to conclude that $σ_1\gtσ_2$
Work Step by Step
$H_0:~σ_1=σ_2$ versus $H_1:σ_1\gtσ_2$
$F_0=\frac{s_1^2}{s_2^2}=\frac{12.3^2}{8.7^2}=2.00$
$d.f_1=n_1-1=24-1=23$
$d.f_2=n_2-1=27-1=26$
Right-tailed test:
$F_{α,n_1-1,n_2-1}=F_{0.1,23,26}=1.68$
(According to table VIII, for $d.f._1=25$, the closest value to 23, $d.f._2=25$, the closest value to 26, and area in the right tail = 0.1)
Since $F_0\gt F_{α,n_1-1,n_2-1}$, we reject the null hypothesis.
