Critical constants for a test of the hypothesis that the mean $\mu$ and the standard deviation $\sigma$ of the normal $N(\mu ,{\sigma }^2)$ population satisfy the constrains $\mu +c\sigma \le M$, $\mu -c\sigma \ge m$, are presented. In this setup $m<M$ are prescribed tolerance limits and $c>0$ in a chosen constant.

The rank statistic $H$ based on the number of exceeding observations in two samples is suitable for testing difference in location of two samples. This paper contains tables of one-sides significance levels $P\{H\ge k\}$ for $k=7,8,...,11;max(2,n-10)<m\le n\le 25,k=9,10,...,13;max(2,n-15)<m\le n-10;13\le n\le 25;k=11,12,...,15;2<m\le n-15,18\le n\le 25$, which includes almost all practically used significance levels for $3\le m\le n\le 25$, where $m,n$ are the sample sizes.