Tests of Significance for the Average Square Deviation from Target in a Finite Lot

Consider lots of discrete items 1,2,...,N with quality characteristics "x1", "x2",...,"xN". Let "a" be a target value for item quality. Lot quality is identified with the average square deviation (formula) from target per item in the lot (lot average square deviation from target). Under economic considerations this is an appropriate lot quality indicator if the loss respectively the profit incurred from an item is a quadratic function of "x1" minus "a". The present paper investigates tests of significance on the lot average square deviation "z" under the following assumptions: The lot is a subsequence of a process of production, storage, transport; the random quality characteristics of items resulting from this process are i.i.d with normal distribution N("u,o"); the target value "a" coincides with the process mean "u"