I'm studying all statistics by Wasserman and on page 156 he defines p-values:
10.11 Definition. Suppose that for every $\alpha \in (0,1)$ we have a size $\alpha$ test with rejection region $R_{\alpha}$. Then,
$$\text{p-value} = \inf\{\alpha: T(X^n)\in R _{\alpha}\}$$
That is, the p-value is the smallest level at which we can reject $H_0$.
Suppose I have $x^i$ the realization of $X^n$, how do I calculate its p-value using this definition? I'm a little confused because the definition doesn't mention when the observed values come into play.