A one-sided confidence set hidden under a two-sided sequential test of a normal mean

This article demonstrates how to construct a 1 - alpha level confidence set naturally associated a size a two-sided sequential test of a normal mean mu. If the null hypothesis H-0: mu = 0 is rejected by the test, then the confidence set provides a one-sided confidence interval excluding zero for mu. Therefore, based on this confidence set, we can not only reject H-0, infer the direction (mu > 0 or mu < 0) of mu, but also have the extra information on the magnitude of mu in the direction of inference. The confidence set is clearly more informative than the original test. (C) 1999 Elsevier Science B.V. All rights reserved.