Prove Theorem 9.7.5. Also, compute the p-value for Example 9.7.4 using the formula in Eq. (9.7.8).
In Theorem 9.7.5.
P-Value of Equal-Tailed Two-Sided F Test. Let V be as defined in (9.7.4). Suppose that we wish to test the hypotheses (9.7.7). Let δα0 be the equal-tailed two-sided F test that rejects H0 when V ≤ c1 or V ≥ c2, where c1 and c2 are, respectively, the α0/2 and 1− α0/2 quantiles of the appropriate F distribution. Then the smallest α0 such that δα0 rejects H0 when V = v is observed is
2 min{1− Gm−1, n−1(v), Gm−1, n−1(v)}. (9.7.8)