I have a two part question;
I have an urn with 20 balls, 2 of those balls are purple, and I pull out 6 balls at random. I witness 100 realizations of this process.
Given the observed frequency at which I drew purple balls, how do I determine if I am really pulling balls out at random? Also given that there are 2 purple balls, I have a hunch that if purple balls are pulled out disproprionately, I expect that both purple balls would be pulled out (i.e. I'm more interested in seeing if 2 purple balls are pulled out disproportionately than I am if 1 purple ball is pulled out more frequently than expected).
I have an urn with a variable number of balls, a variable number of purple balls within that urn, and a variable number of draws. I witness 100 realizations of this process, and I observe in each realization how many balls there were, how many of those balls were purple, and how many balls I drew from the urn.
Same questions; Given the observed frequency at which I drew purple balls, how do I determine if I am really pulling balls out at random? Again I'm more interested to see if higher frequencies of purple balls are disproportionately drawn than I am to see if 1 purple ball being drawn happens more than expected by chance.
(I'm open to suggestions for title of question and tags)
Srikant suggested I may need to make distributional assumptions about my variables, which I am willing to do.
Lets say the number of balls in the urn is uniform between 20 and 30, the number of purple balls is uniform between 0 and 4, and the number of draws is uniform between 6 and 12.
See my answer that describes my motivation for asking this question.