Let's assume a test statistics having "asymptotic normality", the $N(0,1)$ becomes my test distribution.
I also have a hypothesis where $H_0$ is: $P=\text{parameter (from MLE)} = P_0$ true parameter from $H_0$.
$$\frac{P - P_0}{\sqrt{P(1-P)/n}}$$
(the variance under the division is derived from Fisher expected info)
I struggle to see what the term "under $H_0$" have to say for the normality part, except I get two parameters are very close in distance.
What "tools" may I use to show my test statistics conforms to asymptotic normality (important->) assuming null hypothesis is true.
Thank you!