Table 1.

The Niles, IL, computation

m	P(14400, 9000, m)	Monte Carlo	P value
6	0.000005	0.000	1.000000
7	0.095395	0.096	0.999995
8	0.664954	0.678	0.904605
9	0.937864	0.944	0.335046
10	0.990843	0.993	0.062136
11	0.998788	0.998	0.009157
12	0.999852	0.999	0.001212

The computation of the exact values required <5 sec on a personal computer running algebra system Maple (available from the authors upon request). The Monte Carlo computations required ≈30 min. In both the Monte Carlo simulations and the exact calculations, we observed the expected rapid change of P values as m increases, emphasizing the need for exact P value calculations as disscussed in the text.