A problem with a practical application of Varian.s Weak Axiom of Cost Minimization is that an observed violation may be due to random variation in the output quantities produced by firms rather than due to inefficiency on the part of the firm. In this paper, unlike in Varian (1985), the output rather than the input quantities are treated as random and an alternative statistical test of the violation of WACM is proposed. We assume that there is no technical inefficiency and provide a test of the hypothesis that an observed violation of WACM is merely due to random variations in the output levels of the firms being compared.. We suggest an intuitive approach for specifying a value of the variance of the noise term that is needed for the test. The paper includes an illustrative example utilizing a data set relating to a number of U.S. airlines.