Accurate detection of excess over a standard based on a random sample

A known number N of packages each contain, in differing unknown amounts, both substances of no particular import and some substance of interest, the total weight of the latter substance for all N of the packages being an unknown quantity T. Based on the amounts of the substance of interest found in each of n (n ≦= N) randomly sampled packages one is to decide, with a very small probability of the error of wrongly deciding that T exceeds L, whether or not the quantity T exceeds a given amount L. An optimal way of doing this is presented in which the probability of the error of wrongly deciding that T exceeds L can be precisely bounded above as desired.