Implications of sampling from a log-normal population

The environmental radioactivity surrounding the Lawrence Livermore Laboratory is typically log-normally distributed. The geometric standard deviation of radioactivity in all types of samples--air, water, soil, sewage, and vegetation--is about two. Hypothesis testing was done using the mean geometric standard deviation of these samples. Parametric studies demonstrated the effect of the number of background samples, the magnitude of tolerable errors, the variability of the sample population, and the precision of the analysis on the detectability of differences from natural and global fallout radioactivity. It was decided to accept an error probability of 50 percent that the analysis would show a sample to be different from background when, in fact, it was not, and an error probability of 5 percent that the analysis would show a sample to be background, when in fact, it was not. For these assumptions, an analysis must differ from background by a factor of 1.6 to indicate a statistical difference, and a sample must contain radioactivity a factor of 8.6 different from background to be 95 percent detectable with 50 percent confidence. The difference in the mean of two such populations which is 95 percent detectable with 50 percent confidence is 2.8 if six samples are taken from each population