A researcher compares the variability of scores from two independent samples drawn from normal populations. The sample variances are $s_1^2$ and $s_2^2$. She defines the $F$ test statistic as $F=\frac{s_l^2}{s_s^2}$, where $s_l^2$ is the larger of the two sample variances.

True or False: The resulting $F$ statistic can ever be less than $1$.

Two samples with sizes $n_1=980$ and $n_2=1125$ are being compared using an $F$ test for equality of variances. Is it appropriate to ignore the assumption of normality due to the large sample sizes?

Two independent samples yield sample variances $s_1^2=4.9$ with $n_1=15$ and $s_2^2=2.5$ with $n_2=12$. Find the value of the $F$ test statistic for testing equality of population variances (use the convention that the test statistic is at least $1$).

Researchers are studying blood lead levels in two groups: children living near a highway with $n=35$, $\bar{x}=8.2\mu \text{g/dL}$, and $s=3.9\mu \text{g/dL}$, and children living in rural areas with $n=35$, $\bar{x}=2.7\mu \text{g/dL}$, and $s=1.6\mu \text{g/dL}$. At the $0.05$ significance level, test the claim that the variation in blood lead levels is greater for children living near the highway than for those in rural areas.

Determine the critical $F$-value for a right-tailed test with a value $\alpha =0.025$, numerator degrees of freedom value of $d.f.N=4$, and denominator degrees of freedom value of $d.f.D=10$.