Supplement to Letter from R. 0. Gilbert to T. McCraw dated September 22, 1976 Concerning Sampling Pians for Enewetak Cleanup Survey. I. Confidence Limits on True Average (Median) Concentration. x Pu concentration y log, x ot tee lf x is distributed lognormally, then — tS) _ 7. Probfy s y + Tn = J-a it where s ; (since the y, are normal), standard deviation of the y's. y = mean of logs of the sample data, y = true (unknown) mean of logs t = "t" value for specified a and n-1 degrees of freedom. Then exp(y+ ts/yn) is an approximate (l-a)% upper limit on the median of the lognormal distribution (original data). The median is that con- centration above which and below which half the observations lie. For Janet (data taken from Fig. B.8.1.i in NVO-140) we have n= 139, y = 2.180, and s = 1.152 For a= 0.01, 0.05, and 0.10 we find: . a 01 £05 10 Interpretation: " t138 2.35 1.66 1.29 100 (1-a)% Upper Limit on Median 11 pci/g 10 10 For a = .01 we state: We are 99% sure that the true (unknown) median Pu concentration on Janet is less than or equal to 11 pCi/g (if the data are lognormal). Discussion: An alternative approach would be to assume the mean x of the Pu concentrations is approximately normally distributed. Then an upper confidence limit on the true (inknown) mean would be computed as x + a » where s now refers to the standard devia- tion of the original untransformed observations. Since for Janet we have n = 139, x = 15.9 pCi/g, s = 20.9 pCi/g we find the approximate limits: