The Wald test:

\[ \mathcal{WS}(\theta_{0})=(\hat{\theta}-\theta_{0})'\left(\dfrac{\hat{J_{2}}}{n}\right)^{-1}(\hat{\theta}-\theta_{0}) \]

The Score test:

\[ \mathcal{SCR}=n\left(\dfrac{1}{n}\sum_{i=1}^{n}s(w_{i},\theta_{0})\right)'\hat{J_{2}}^{-1}\left(\dfrac{1}{n}\sum_{i=1}^{n}s(w_{i},\theta_{0})\right) \]

The likelihood ratio test:

\[ \mathcal{LR}=2\left(\sum_{i=1}^{n}\ln f(w_{i}|\hat{\theta})-\sum_{i=1}^{n}\ln f(w_{i}|\theta_{0})\right) \]

These tests are compared to a $ \chi^{2} $ at the 5\% significance level.Thus $ \chi^{2}(1)=3.841 $.