Direct Methods for Exact Truncated Seyuential Tests of the Mean of a Normal Distribution

Abstract

This paper gives tables of the exact operating characteristic (O. C.) function, of the exact average sampler number (A. S. N.) function, and of the probability of termination at any step for certain one-sided truncated sequential tests of the mean of a normal distribution when the variance is known. By looking at the smallness of the probability that a sequential test terminates after the equivalent fixed sample test it is observed that truncated sequential tests are more economical over a wider range of possible values of the mean than previously recognized. The O. C. and A. S. N. tables presented here may be used for approximate two-sided truncated sequential tests in the same manner as in [7]. Also, the scope of thii paper is contrasted with the work of other authors. Aroian's direct numerical methods are used [2]. These methods emphasize the use of digital computers to calculate the distributions of those test statistics required for computation of the operating characteristic (O. C.) function and the...