How can I show that $\dfrac{\hat{\rho } \sqrt{N-2}}{\sqrt{1-\hat{\rho}^2}}$ has a t-student distribution with $N-2$ degrees of freedom.
I think I have to write it as a quotient of a normal $(0,1)$ and the squared root of a chi-squared distribution divided in its df. But I've been trying and could not do it.