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Attachment E-1 Contamination Measurement Methodology: Single Loads <br />REV: 03-16-18 MI <br />ATTY/AGR/2018.054/RECOLOGY OF SAN MATEO ATTACHMENT E <br />Page 8 of 14 <br />The confidence interval for this estimate will be derived in two (2) steps. First, the variance around <br />the estimate will be calculated, accounting for the fact that the ratio included two (2) random <br />variables (the component and total sample weights). The variance of the ratio estimator equation <br />follows: <br /> () <br /> <br /> <br /> <br /> <br /> <br /> <br />− <br />− <br /> <br /> <br /> <br /> <br />≈ <br />∑ <br />1 <br />11)Var( <br />2 <br />2 n <br />wrc <br />wnr i <br />ijij <br />j <br /> <br />(2) <br />where: <br />w <br />w <br />n <br />i <br />i= <br />∑ <br /> <br />(3) <br />(For more information regarding Equation 2, please refer to Sampling Techniques, 3rd Edition by <br />William G. Cochran [John Wiley & Sons, Inc., 1977].) <br />Second, precision levels at the 90 percent (90%) confidence level will be calculated for a <br />component’s mean as follows: <br /> ())Var(jjrzr± (4) <br />where z = the value of the z-statistic (1.645) corresponding to a 90 percent (90%) confidence <br />level. <br /> <br /> <br />6.2.B. - Page 169