I seem to be confused on what is the utility of calculating the p-value.
Let's say for the sake of argument, that I'm doing hypothesis testing on a normal distribution with a known $\mu$ and known $\sigma$. We have the sample therefore we also computed the sample mean.
I would therefore compute my test statistic: $$ \dfrac{\overline X - \mu}{\dfrac{\sigma}{\sqrt{n}}}$$
and see if it falls within the area between $Z_{-\alpha/2}$ and $Z_{\alpha/2}$. If it doesn't we reject the null hypothesis.
Now what is the point of calculating the p-value if we can do this. When is it appropriate to use the p-value instead for accepting or rejecting the null hypothesis.