Wilcox (1977) examines two methods of estimating the probability of a false-positive on false-negative decision with a mastery test. Both procedures make assumptions about the form of the true score distribution which might not give good results in all situations. In this paper, upper and lower bounds on the two possible error types are described which make no assumption about the form of the true score distribution. Illustrations are given on how these bounds might be used to determine the length of the test.