Hypothesis tests are commonly framed as
$H_0: p_0 = p_1$ vs. $H_1: p_0 \not= p_1$.
But I am interested in the case:
$H_0: |p_0 - p_1| < c $ vs. $H_1: |p_0 - p_1| \ge c $
for some constant $c$.
Could I apply a likelihood ratio test? - the degrees of freedom would be the same in both cases, I suppose?
Would I have to go Bayesian and apply an (arbitrary) prior?