How much sample size is required to estimate the true arithmetic mean of a lognormal distribution?

The exact minimum required sample sizes for estimating the arithmetic mean of a lognormally distributed random variable are based on its exact confidence interval width. These exact values are given for a specified accuracy or percent difference from the true arithmetic mean for different geometric standard deviations within a specified level of confidence. Percent differences between upper and/or lower confidence limits and the true arithmetic mean were computed and sample sizes were calculated using Land's exact method for computing confidence intervals for the arithmetic mean. Tables and nomograms are presented. Monte Carlo estimates of coverage probabilities show the appropriateness of theses exact proposed samples sizes at the 95% confidence level. Box-Cox transformations were used to derive formulae for approximating these exact sample sizes. New formulae, adjusting the classic limit approach were also determined. Each of these formulas as well as other existing formulas were compared to the exact sample size to establish under which conditions they perform optimally and recommendations are presented.