LetXdenote the number of itemsdeclareddefective in a sample of sizenselected without replacement from a batch ofNitems containing θ defectives, where testing is fallible. In this note it is shown that the density ofX,p(x, θ), has a monotone likelihood ratio (MLR) inx, and the relevance of this fact to inference is discussed in detail. In addition, an interesting connection is made between the MLR property and the suitability ofXas a proxy for the “true” number of defectives in regression modeling.