Consideration of a situation where a stochastic process starting at time t = 0 is observed. A continuous sequential test of simple hypotheses concerning the underlying distribution of the process is performed. A choice is then made between the alternate hypotheses in accordance with the test procedure, which is, in fact, designed to produce this choice within specified probabilities of error. The experimenter may wish to know, however, if he can also use his knowledge of the test duration to increase his knowledge of the underlying distribution of the process. This paper demonstrates that, for a sequential probability ratio test (SPRT), he cannot do so.