7.3.10. Suppose that two independent samples of size $n$ are drawn from a normal distribution with variance $\sigma^2$. Let $S_1^2$ and $S_2^2$ denote the two sample variances. Use the fact that $\frac{(n-1)S^2}{\sigma^2}$ has a chi square distribution with $n - 1$ df to explain why $\lim_{\substack{n \to \infty \ m \to \infty}} F_{m, n} = 1$
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The F-statistic is calculated as the ratio of the sample variances: F = S1^2 / S2^2 Show more…
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