As an alternative to a classical test theory basis for criterion-referenced test construction, it is proposed that a strict item-sampling model be used. The computer's role in such a model is outlined. The assumptions of the model are carefully defined and its properties reviewed. The relationship between mastery criteria and such sampling plans as single sampling, simple curtailed sampling, and the use of the sequential probability ratio test is discussed. Representative operating characteristic curves for a number of different plans are included. Suggestions are offered for reducing the testing time needed to detect mastery attainment levels which are consistent with the Newman-Pearson theory of hypothesis testing. Applications are indicated, and an example included, in the area of computer-generation and administration of criterion-referenced tests of mastery in selected arithmetic skills. (DG)