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<br />The confidence interval for this estimate will be derived in two (2) steps. First, the <br />variance around the estimate will be calculated, accounting for the fact that the ratio <br />included two (2) random variables (the component and total sample weights). The <br />variance of the ratio estimator equation follows: <br /> <br />(1)( 1 )[~ (Cij - rjwJ] <br />Var(r.) ~ - - <br />) n w2 n-1 <br /> <br />(2) <br /> <br />where: <br /> <br />LW; <br /> <br />W = ; <br />n <br /> <br />(3) <br /> <br />(For more information regarding Equation 2, please refer to Sampling Techniques, 3rd <br />Edition by William G. Cochran [John Wiley & Sons, Inc., 1977].) <br /> <br />Second, precision levels at the 90 percent (900/0) confidence level will be calculated for a <br />component's mean as follows: <br /> <br />rj I (z~Var(rj)) (4) <br /> <br />where z = the value of the z-statistic (1.645) corresponding to a 90 percent (900/0) <br />confidence level. <br /> <br />Facility Agreement, Attachment 2E <br />Contamination Measurement Methodology <br />Page 9 of 15 <br />