chi-square and normal distribution

Hi. I have this problem.

Making use of the fact that the chi-square distribution can be approximated by

a normal distribution when $\displaystyle v$, the number of degrees of freedom, is large,

show that for large samples from a normal population,

$\displaystyle s^2 \ge \sigma_0^2[1+z_{\alpha}\sqrt{\frac{2}{n-1}}]$

is an approximate critical region of size $\displaystyle \alpha$ for testing $\displaystyle H_0:\sigma^2=\sigma_0^2$ against $\displaystyle H_1:\sigma^2> \sigma^2$

Thanks.