Supplement to Letter from R. 0. Gilbert to T. McCraw dated September 22, 1976 Concerning Sampling Plans for Enewetak Cleanup Survey. I. Confidence Limits on True Average (Median) Concentration. x Pu concentration y log, x - ue If x is distributed lognormally, then Prob[p < y +48 = |-a (since the y; are normal), where s = standard deviation of the y's. y = mean of logs of the sample data, u = true (unknown) mean of logs t = "t" value for specified a and n-] degrees of freedom. Then exp(y + ts/vn) is an approximate (1-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: 100 (1-a)% Upper _o O01 ti38 2.35 05 1. 66 10 -10 1.29 10 Interpretation: Limit on Median 11 pCi/g 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 + ‘8 » 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: