2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/85415In this paper, after a discussion of general properties of statistical tests, we present the construction of the most powerful hypothesis test for determining the existence of a new phenomenon in counting-type experiments where the observed Poisson process is subject to a Poisson distributed background with unknown mean.8 pages, 1 figure, submitted to PRDData Analysis, Statistics and ProbabilityAstrophysicsHigh Energy Physics - Experimenttext