When Zero Defectives Appear in a Sample: Upper Bounds on Confidence Coefficients of Upper Bounds

When zero defectives are observed in a sample from a finite universe, investigators and decision makers are often tempted to (and want to) declare that there are zero defectives in the finite universe with high confidence.By focusing on the more general question of upper bounds for confidence coefficients of upper confidence bounds, as a special case we are able to show explicitly that our confidence that there are zero defectives in the universe when zero defectives appear in the sample is bounded by the sampling fraction.This note is meant to help reassure those who seek to help others yield not to the aforementioned temptation.