Honest question: suppose I pick a plausible sounding h(x), perform the proposed test, and get a vanishingly small p-value. So I feel pretty happy about rejectin

Honest question: suppose I pick a plausible sounding h(x), perform the proposed test, and get a vanishingly small p-value. So I feel pretty happy about rejecting the null hypothesis. But the null hypothesis is a conjunction: A group members accepted have cdf a(x), B group members accepted have cdf b(x), and h(x) satisfies various technical conditions related to a( ) and b( ). So when I reject the null, I'm saying the data were unlikely to be generated by the hypothesized process. Couldn't that simply be because I guessed the wrong form of h( )?