Statistical Computing and Graphics Calculation of Hypergeometric Probabilities Using

Using Chebyshev polynomials we generate an algorithm for the efficient calculation of hypergeometric probabilities. For a fixed population size N and fixed sample size n, such cal- culations simultaneously produce distributions for all pos- sible values of the population number of "successes" M. sponding to the values of M1 and M2, the hypergeometric distribution is used to find the values of c and n that satisfy the requirements. In another situation, for a fixed lot size N, a sample of size n is taken, and the number of defec- tives 2 is observed. Hypergeometric probabilities are used to construct confidence intervals for the unknown number of defectives M. Fisher's exact test for independence in a simple 2 x 2 contingency table, can also be applied to a test of homogeneity of the proportion of defectives in two populations (see Kendall and Stuart 1979, p. 580). In such a situation, random samples of size n1 and 722 items are taken from each population, giving x1 and 22 defectives, respec- tively. Critical values for the test require hypergeometric probabilities with parameter values N = n1 + n2, M = n1, and n = XI+ 22.