Suppose I have two independent events that occur with unknown probabilities. For example, I have two buttons, and each time I press a button there is an unknown chance that it will make a noise.
I want to know if the probability that the two buttons make a noise is the same, so I run some tests.
I press Button A 100 times, and it makes a noise 6 times (6%). I press Button B 200 times, and it makes a noise 16 times (8%).
From this, I don't know if Button B actually has a higher chance of making the noise, or it was just luck.
I want to do a hypothesis test with the null hypothesis that both buttons do have the same chance of making a noise. I'm not sure where to start though, how can I test this?