Hypothesis testing and estimation for air contaminants

This paper deals with the problem of enforcing standards of maximum allowable atmospheric contaminants. This enforcement has to be done by deciding whether the actual level of contaminant is in violation or compliance with the standards. Due to inherent uncertainties, a decision is to be made only if the probability of error is below a prescribed level. The measurements of contaminant are modeled as a set of lognormal random variables with unknown mean and variance. A uniformly most powerful unbiased test is developed to test their mean against a given threshold. It is shown that the test can be carried out in a very simple manner with the help of a decision chart. This is done by plotting a point defined by the sufficient statistics of the observations and reading off the decision. The estimate of the actual level of contaminant is also discussed.