This Demonstration performs a goodness-of-fit test on a set of random samples of a given sample size from a finite population. The count for each subset is indicated by a point; the expected value is indicated by the horizontal line. Tooltips on each show the values. The "trial" slider controls a seed for the random number generator, and gives a new set of samples for each value. The -value () is the probability that another set of truly random samples would be as far or farther away from the expected value (as measured by ).
This Demonstration shows that the random sample function in Mathematica seems to choose each possible sample with (at least approximately) equal likelihood. The -value ranges over the interval [0,1]. This Demonstration does not show that the -values have a uniform distribution, but a user could keep track of the -values and plot his or her own distribution.