I've been researching the deep underlying mathematics of A/B testing. I understand A/B tests to be Bernoulli trials (conversion / non conversion) and categorical data represented in a 2x2 contingency matrix.
Why and how is it that many blogs or websites recommend using a Z-test to measure whether the two sample frequencies are drawn from the same population (accept null hypothesis), or are significantly different meaning they're drawn from different populations (reject null hypothesis)? How can a Z-test even be applied here?
This Wikipedia page doesn't list Z-test for categorical data: http://en.wikipedia.org/wiki/List_of_analyses_of_categorical_data
I understand that a G-test or Chi-square test is suitable, but does not provide a confidence interval, only a p-value to compare to a significance level. Is this related?