A criterion-referenced computerized test is expressed as a statistical hypothesis problem. This admits that it can be studied by using the theory of optimal design. The power function of the statistical test is used as a criterion function when designing the test. A formal proof is provided showing that all items should have the same item characteristics, i.e. items that have high discrimination, low guessing and difficulty near the cut-off score give the most powerful statistical test. An efficiency study shows how many times more items are needed if nonoptimal items are used instead of optimal items in order to get the same power in the test. (Contains 4 figures.)