I want to calculate a sample size for a large population of about 50 million. I came across Cochran's formula and the finite population correction. In short, Cochran's formula is the following:
$$ n_\infty = \frac{z^2 p(1-p)}{e^2} $$ I have found multiple resources that describe p as a sample proportion or as estimated proportion of an attribute that is present in the population. Most of the time, p is considered by default 0.5.
1) What is p and how can I understand it intuitively with an example?
2) Is p found exclusively via experiments? If not, what is its formula?
3) Most people use p = 0.5 because it gives the maximum sample size. Is this true?