I was testing whether the proportion of successes from two populations is the same. It made me realize I only know how to do this with a normal approximation.
In particular, I would like to solve Exercise 9.3 from this set of exercises using a binomial distribution.
I understand that you may not feel like checking out my GitHub, so here's my problem in more general terms: suppose I flip a coin 100 times to test the hypothesis that the coin is unbiased. Instead of comparing the observed number of successes against the expected number of successes under $H_0$, I want to compare the observed proportion of successes against the expected proportion of successes. How can I test this without a normal approximation?
I found a post that suggests using Fisher's exact test. This is helpful in that it skips the normal approximation, but can this be done using a binomial test?