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• <br />• <br />Directions for Land's Method are contained in Box 3 -11, with an example in Box 3 -12. <br />Box 3 -11: Directions for Computing Confidence Limits for the Population <br />Mean of a Lognormal Distribution Using Land's Method <br />COMPUTATIONS: Transform the data: y, = In x,, i = 1,...,n. Next, compute the sample mean, y , and sample <br />variance, s3, of the transformed data. The values for H and H come from Table A -17. <br />2 <br />An upper one -sided 100(1 - a)%o confidence limit for the population mean is ex y + s { s y H �_ a <br />2 n 11 <br />/ 2 \ <br />A lower one -sided 100a% confidence limit for population mean is exp y + s + s Y H a <br />2 Jn -1 / <br />Box 3 -12: An Example Using Land's Method <br />A random sample of 15 concentrations from a monitoring process (assumed to be lognormal) is reported: <br />8.12, 7.32, 4.82, 6.52, 7.80, 11.89, 12.94, 7.51, 18.14, 4.09, 5.70, 15.57, 6.68, 8.15, 5.56. <br />Compute an upper one -sided 95% confidence limit for the population mean of the process. <br />COMPUTATIONS: The log- transformed data set is: <br />2.09, 1.99, 1.57, 1.87, 2.05, 2.48, 2.56, 2.02, 2.90, 1.41, 1.74, 2.75, 1.90, 2.10, 1.72 <br />The sample mean and sample standard deviation of the transformed data are y = 2.0767 and s = 0.4272 . <br />The value of H0 is found by interpolation in Table A -17. <br />An upper one -sided 95% confidence limit for the population mean is <br />exp) y - s y + s y HO 96 \ _ exp 2.0767 + 0.4272 + 0.4272.1.9939 10.97 <br />I 2 n -1 2 14 <br />