Hypothesis Testing with Interval Data: Case of Regulatory Constraints

In many practical situations, there exist regulatory thresholds: e.g., a concentration of certain chemicals in the car exhaust cannot exceed a certain level, etc. If we know the exact value of the corresponding quantity, then we can immediately tell whether, e.g., a car design resulting in this value is acceptable (below the threshold) or not acceptable (above the threshold). In practice, however, the value of the desired quantity comes from measurements or from expert estimates; in both cases, the resulting estimates are not 100% accurate. It is therefore necessary to make an accept/reject decision based on this estimate, i.e., based on the approximate value of the quantity.A similar situation occurs when instead of the exact threshold, experts provide us with an imprecise threshold like "about 140". In this paper, we describe how to make accept/reject decisions under measurement or expert uncertainty in case of regulatory and expert-based thresholds, where the threshold does not come from a detailed statistical analysis.