Past exam of the mathematics course of the University of Cambridge / 2022 / ib / Paper 3 / 18H / d / Solution

Let $\nu =n/2-p$. Under $H_0$, the two residual sums of squares are independent and satisfyHenceUnder $H_1$, the numerator is scaled by the smaller variance, so small values provide evidence against the null. If $F_{\nu ,\nu }^{-1}(\alpha )$ denotes the lower $\alpha$ quantile, a size-$\alpha$ test rejects when