The critical value for a two-tailed $F$ test is $2.65$ when $\alpha = 0.05$, the sample size from which the variance for the numerator was obtained is 10 , and the sample size from which the variance for the denominator was obtained is 15 .

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The critical value for an $F$ test depends on the degrees of freedom for the numerator ($df_1$) and the denominator ($df_2$), as well as the significance level ($\alpha$). The degrees of freedom are calculated as $df_1 = n_1 - 1$ and $df_2 = n_2 - 1$, where $n_1$ and $n_2$ are the sample sizes. For this scenario, $df_1 = 10 - 1 = 9$ and $df_2 = 15 - 1 = 14$. The critical value must be looked up in an $F$ distribution table or calculated using statistical software specific to these degrees of freedom and the given $\alpha$, and it is not universally $2.65$ for all combinations of sample sizes and $\alpha$ levels.

The Critical Value for a Two-Tailed FFF Test Is 2.652.652.65 When α=0.05\alpha = 0.05α=0.05

The Critical Value for a Two-Tailed $F$ Test Is $2.65$ When $\alpha = 0.05$