Interval estimation for log‐normal mean with applications to water quality

Large samples based confidence interval is frequently used by environmental scientists as an approximate data summary about the log‐normal regression mean. It has been shown by simulation that the coverage probability of such an interval is below the intended nominal level for small samples. To overcome this difficulty, a complicated small sample corrected interval has been recently proposed in the literature which substantially improves the coverage probability. In this paper, similar improvement are obtained by simply replacing the quantile of the normal distribution by the appropriate quantile of Student t distribution as will be demonstrated in this paper by simulation. The advantage of our proposed interval is its simplicity and thus will be easier to use in applications. As an illustration, we use the method to study the relationship between the flow and concentration of total phosphorous (TP) at four upstream/downstream sampling locations on the Fraser River of British Columbia. Our interests in developing intervals for the mean TP level at each location as well as the ratio of the mean at a downstream location to that at an upstream location. Such study is important in tracing the evolution of pollutants in an ecosystem and thus in setting policies for pollution control.