During the past 25 years much attention has been given by prominent statistical writers, especially J. Neyman and E. S. Pearson, to building up the theory of the Testing of Statistical Hypotheses. This theory and the practical tests which have been developed from it are of great interest to actuaries, those employed in normal actuarial spheres as well as those employed in purely statistical roles. The leading exponents of the theory, however, are mathematicians of no mean standing and the subject has been approached from a mathematical angle. From the point of view of the actuary or student whose study of mathematics has not proceeded beyond that of the Institute's examination syllabus this is unfortunate, as the consequent complexity of the approach masks from him the essential simplicity of the basic ideas underlying the theory.