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 the standard deviation walking speed is different between the two groups.
Work Step by Step
$H_0:~σ_1=σ_2$ versus $H_1:σ_1\neσ_2$
$F_0=\frac{s_1^2}{s_2^2}=\frac{53^2}{34^2}=2.43$
$d.f_1=n_1-1=260-1=259$
$d.f_2=n_2-1=269-1=268$
Two-tailed test:
$F_{\frac{α}{2},n_1-1,n_2-1}=F_{0.025,259,268}=1.37$
(According to table VIII, for $d.f._1=120$, the closest value to 259, $d.f._2=200$, the closest value to 268, and area in the right tail = 0.025)
$F_{1-\frac{α}{2},n_1-1,n_2-1}=F_{0.975,259,268}=\frac{1}{F_{0.025,259,268}}=\frac{1}{1.37}=0.73$
Since $F_0\gt F_{\frac{α}{2},n_1-1,n_2-1}$, we reject the null hypothesis.
