True. You have seen in lesson 86 — hypothesis tests on the proportion, that the null distribution is a Binomial distribution with n, the sample size, and p, the proportion being tested.

You have seen in lesson 87 — hypothesis tests on the mean, that the null distribution is a T-distribution because

You have seen in lesson 88 — hypothesis tests on the variance, that the null distribution is a Chi-square distribution because

Did you ever wonder what if the test statistic is more complicated mathematically than the mean or the variance or the proportion and if its limiting distribution or the null distribution is hard to derive?

Or, did you ever ask what if the assumptions that go into deriving the null distribution are not met or not fully satisfied?