This article explains the rationale of controlling the risk of a type II error for substantive tests in auditing. The risk of attesting to a materially misstated amount is defined in one of two ways depending on the combination of decision strategy and sampling plan in use. When employing difference estimation, the auditor makes an interval estimate of the amount of error in an account balance. If the upper precision limit is less than the amount considered material, the book value is accepted. Here the risk to be controlled is one minus the confidence level employed, i.e., the probability of a Type I error. The more popular strategy, at least as far as textual treatments are concerned, involves making an interval estimate of the audited value of an account balance and accepting the book value if it falls within the interval. The audit examination is quite analogous to the quality control example. If an auditor accepts a book value only if it falls within his interval estimate of the "true" value, the adverse consequences of a Type I error are primarily the costs of extended audit procedures.

Lawrence D. Jones, R. Richardson Pettit, The Role and Viability of Mutual Banks, The Journal of Finance, Vol. 30, No. 2, Papers and Proceedings of the Thirty-Third Annual Meeting of the American Finance Association, San Francisco, California, December 28-30, 1974 (May, 1975), pp. 677-679

This paper presents estimates of partial elasticities of substitution among reproducible capital, labor, and an input aggregate of natural resource products. We are specifically interested in two hypotheses: (i) Are natural resource products strictly complementary in production with either capital or labor? (ii) Are resource products typically less substitutable with capital than with labor? To both questions the answer is, generally, no. Two modes of investigation are used, one based on a translog production function and the other making use of a translog cost function. For most industry groups, the estimated substitution elasticities obtained from the cost function are somewhat lower than those based on the translog production function.