# Math Help - Relationship between t-test and Chi-squared

1. ## Relationship between t-test and Chi-squared

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 $\Phi (1.96) = 0.975$, i.e. $z_{0.025} = 1.96,$ and $\chi^2_{0.05}(1) = 3.841 = (1.96)^2$.

Also

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

2. Originally Posted by Deadstar
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 $\Phi (1.96) = 0.975$, i.e. $z_{0.025} = 1.96,$ and $\chi^2_{0.05}(1) = 3.841 = (1.96)^2$.
The square of a standard normal RV has a $\chi^2$ distribution.

Presumably the same relation holds for t and F distributions (but I do not know that).

RonL