I was rereading some probabilty and statistics chapters from math books and it looks like the *binomial test* is based on the *binomial distribution* and the *t-test* is based on the *student t distribution*.

Does it follow that all hypothesis tests are based on a distribution? Or all distributions have a test based on it? There are other probability distributions such as poisson, bernoulli, geometric, uniformâ€¦

Is there a generalization that can be made with regards to using any kind of distribution to perform a hypothesis test?