THE WAGR SEQUENTIAL t-TEST REACHES A DECISION WITH PROBABILITY ONE'

, and a2 are the mean and the variance of the normal population under test. We prove that, with probability one, a decision is reached when the WAGR test is applied. This fact is of importance in its own right; it also has indirect interest because, unless it were true, the standard Wald inequalities on probabilities of error at the two hypothesis points could not be applied. 1. Introduction. The WAGR sequential test for one-sided proportion defective may formally be described as follows: Let X1, X2, * * be a sequence of independent identically distributed normal random variables with mean u and variance 2 Let U be a given number. Let n n \ 12