The challenge here is to show that

$\displaystyle \left(\frac{n}{p(1-p)}\right)^{\frac{1}{2}}f\left(T_p\right)\left(\ch i _{(p)}-T_p\right)\to Z\sim N(0,1)$

Where convergence here is convergence in law, T_p is the pth quantile of f, where f is the PDF of the F distribution and r/n=p remains fixed. I don't even know where to start! Many thanks to whomever can solve this toughie...