A situation where only the r smallest values of a sample of size n are available is considered. This paper investigates the case where n is large and r is of the form pn 0 square root of n. Properties of some well known estimates and tests of the 100p population point based on statistics of the type used for the sign test are investigated. If the sample is from a normal population, these non-parametric results have high efficiencies for small values of p at least 95 if p or 110. Asymptotically best estimates and tests of the population percentage points are derived for the case where the population variance is known. The results of the paper have application in the field of life testing.