Let be independent identically distributed random variables each with normal distribution with mean and variance . Tests for the process mean are well-known elements of statistical analysis: the Gauss test under known process variance , Student's t-test under unknown process variance . Let the process be partitioned in lots , , of size N. Consider as a stochastic representative of this lot sequence and let the lot be characterized by the lot mean . The lot mean can be considered as a parameter of the joint conditional distribution function of the lot variables under . The present paper investigates the analogies of the Gauss test and Student's t-test for the lot situation, i.e. tests of significance for the lot mean z under known and unknown process variance . This approach is of special interest for the statistical control of product quality in situations where the quality of a lot of items with quality characteristics is identified with the lot average .
