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equation. Selected Sampling Approach A parametric random sampling approach was used to determine the number of samples and to specify sampling locations. A parametric formula was chosen because the conceptual model and historical information (e.g., historical data from this site or a very similar site) indicate that parametric assumptions are reasonable. These assumptions will be examined in post-sampling data analysis. Both parametric and non-parametric approaches rely on assumptions about the population. However, non-parametric approaches typically require fewer assumptions and allow for more uncertainty about the statistical distribution of values at the site. The trade-off is that if the parametric assumptions are valid, the required number of samples is usually less than the number of samples required by non-parametric approaches. Locating the sample points randomly provides data that are separated by many distances,whereas systematic samples are all equidistant apart. Therefore, random sampling provides more information about the spatial structure of the potential contamination than systematic sampling does. As with systematic sampling, random sampling also provides information regarding the mean value, but there is the possibility that areas of the site will not be represented with the same frequency as if uniform grid sampling were performed. Number of Total Samples: Calculation Equation and Inputs The equation used to calculate the number of samples is based on a Student's t-test. For this site, the null hypothesis is rejected in favor of the alternative hypothesis if the sample mean is sufficiently smaller than the threshold. The number of samples to collect is calculated so that 1)there will be a high probability (1-0) of rejecting the null hypothesis if the alternative hypothesis is true and 2)a low probability ((x) of rejecting the null hypothesis if the null hypothesis is true. The formula used to calculate the number of samples is: D2 = 2 (Z,-C? +0.5 d +0.51 a A where n is the number of samples, S is the estimated standard deviation of the measured values including analytical error, A is the width of the gray region, a is the acceptable probability of incorrectly concluding the site mean is less than the threshold, R is the acceptable probability of incorrectly concluding the site mean exceeds the threshold, Z"_a is the value of the standard normal distribution such that the proportion of the distribution less than Ziis 1-a, Z,-P is the value of the standard normal distribution such that the proportion of the distribution less than Z1_13 is 1-(3. The values of these inputs that result in the calculated number of sampling locations are: Parameter Analyte n - S A a a R Z1-a Z1-�b TPH 13 2.3 2 0.05 0.1 1.64485 1.28155 a This value is automatically calculated by VSP based upon the user defined value of a. b This value is automatically calculated by VSP based upon the user defined value of R The following figure is a performance goal diagram, described in EPA's QA/G-4 guidance (EPA, 2000). It shows the probability of concluding the sample area is dirty on the vertical axis versus a range of possible true mean values for the site on the horizontal axis. This graph contains all of the inputs to the number of samples equation and pictorially represents the calculation. The red vertical line is shown at the threshold (action limit)on the horizontal axis. The width of the gray shaded area is equal to A; the upper horizontal dashed blue line is positioned at 1-a on the vertical axis; the lower horizontal dashed blue line is positioned at 5 on the vertical axis. The vertical green line is positioned at one standard deviation below the threshold. The shape of the red curve corresponds to the estimates of variability. The calculated number of samples results in the curve that passes through the lower bound of A at R and the upper bound of 0 at 1-a. If any of the inputs