Repeated significance test II, for hypotheses about the normal distribution

For testing H0:μ<0 against H1:μ>0 and against when the observations are independent normal with known variance, tests of the following structure are considered: For fixed n , stop with the first i≤n such that and reject H0, . Otherwise stop with n observations and accept H0 . Bounds on the power function and expected sample size are obtained, and these become exact limits as n→∞. The power function of these tests never falls below 94% of that of the corresponding nonsequential UMP (UMPU) tests.