Let $X_1,...,X_{16}$ a sample of size $n = 16$ from a Z $\sim N(\mu,\sigma^2)$ with $\mu$ and $\sigma^2$ unkown.
Consider the hypothesis testing problem : $$H_0:\sigma^2 = \sigma_0^2 \text{ vs } H_1:\sigma^2 \neq \sigma_0^2 \text{ with }\sigma_0^2 = 15$$
Also we know that our test rejects $H_0$ if the observed value of the sample variance satisfies: $$s_n^2\geq2.0287\cdot \sigma_0^2 \text{ or } s_n^2 \leq 0.3487\cdot \sigma_0^2 $$
Question: Determine the significance level of the test.
My idea:
I know that my statistics is $X_0^2:=\dfrac{(n-1)S_{n}}{\sigma_0^2}$
And i know that we rejects $H_0$ if $x_0^2\geq\chi_{\alpha/2,n-1}^2 \text{ or } x_0^2 \leq \chi_{1-\alpha/2,n-1}^2$.
But i can't figure out how to procede (what's confusing me a lot is what is the $x_0^2$ and how it's related to $s_n^2 $.
Thanks.