Two Variances and F Distribution: Videos & Practice Problems

A quality engineer is comparing the strength variability of steel rods produced by two different rolling mills. From each mill she takes an independent sample of rods, computes the sample variances $s_1^2$ and $s_2^2$, and forms the $F$ test statistic $F=\frac{s_1^2}{s_2^2}$.
True or False: If $F$ is very close to $1$, then the two samples have essentially the same variability.