Use the fact that if is the sample quantile (sample size n) and is the population quantile (both are pth quantile) then asymptotically . You have to standardize it.
The challenge here is to show that
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...