Confidence Interval for the Ratio of Two Normal Variables (an Application to Value of Time)

Abstract

The problem of making inferences about the ratio of two normal variables occurs in many fields such as bioassay, bioequivalence and ecology. In this paper the theory of the ratio of two normal variables is applied in evaluating the value of time, which is a major component in cost-benefit analysis of transport projects. The subjective value of time is the ratio of the marginal rate of substitution between travel time and travel cost. This paper explores the building of confidence intervals for the subjective value of time, applying methods that make inferences about the mean for the ratio of normal variates: direct substitution of Fieller’s pdf and t-test method. In addition, we also propose a method to minimize the length of the confidence interval.