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 [alpha] two-sided sequential test of a normal mean [mu]. If the null hypothesis H0: [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 H0, 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.