This is something that has been pointed out to me but never explained. Any idea how these are linked? Heres the exact question...

It is no accident that $\displaystyle \Phi (1.96) = 0.975$, i.e. $\displaystyle z_{0.025} = 1.96,$ and $\displaystyle \chi^2_{0.05}(1) = 3.841 = (1.96)^2$.

Also

It is no accident that $\displaystyle t_{0.025}(10) = 2.228$, $\displaystyle F_{0.05}(1,10) = 4.965 = (2.228)^2$.