I am confused with calculation of the p-value for binomial hypothesis testing when not using the normal approximation and its Z-statistic.
My hypothesis testing is for the situation when H₀: π = π₀ and H₁: π ≠ π₀. Suppose we have a sample with 101 successes out of 790 trials (π = 12.8%). We also have a reference value π₀ = 11.7% for the supposed population percentage. I want to calculate the exact binomial p-value for two-sided test, and I got stuck in the middle.
First, I consider the binomial distribution B(790, 0.117) and calculate the probability of observing 101 or more successes (right tail). I use Excel formula
=1 - BINOM.DIST(100, 790, 0.117, TRUE) which evaluates to 0.185…, but it is not a question of Excel coding, but the question of the theory of calculating.
My problem is that I don’t fully understand what to do next to arrive at p-value from this 0.185. Some sources suggest that I should multiply this number by 2, but I’m in doubt: since my binomial distribution is not symmetric, I cannot simply double one-tail probability to get the proper two-sided p-value.
I feel like I should calculate some other probability for the same binomial distribution and add it to 0.185 go get the p-value, but probability of what exactly should it be? Please help me to find out.