  For one-sample level $\alpha$ tests $\psi_m$ based on independent
observations $X_1,...,X_m$, we prove an asymptotic formula for the actual level
of the test rejecting if at least one of the tests $\psi_{n},...,\psi_{n+k}$
would reject. For $k=1$ and usual tests at usual levels $\alpha$, the result is
approximately summarized by the title of this paper.
  Our method of proof, relying on some second order asymptotic statistics as
developed by Pfanzagl and Wefelmeyer, might also be useful for proper
sequential analysis. A simple and elementary alternative proof is given for
$k=1$ in the special case of the Gauss test.
