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change, the number of samples that result in the correct curve changes. 1-Sample t-Test of True Mean vs. Action Level 1 n=13 al ha=5%,beta=10%,std.dev.=2.3 0.9 i J � Q 0.8 I- I I /A 0.7 I- d E 0.6 - 0.5 L-- a 0.4 — w 0.3 ca p 0.2 r- a i 0.1 ---- - - ----- oT 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 True TPH Mean Statistical Assumptions The assumptions associated with the formulas for computing the number of samples are: 1. the sample mean is normally distributed (this happens if the data are roughly symmetric and the sample size is 30 or more- for skewed data sets, additional samples are required for the sample mean to be normally distributed), 2. the variance estimate, S2, is reasonable and representative of the population being sampled, 3. the population values are not spatially or temporally correlated, and 4. the sampling locations will be selected randomly. The first three assumptions will be assessed in a post data collection analysis. The last assumption is valid because the sample locations were selected using a random process. Sensitivity Analysis The sensitivity of the calculation of number of samples was explored by varying the standard deviation, lower bound of gray region (% of action level), beta (%), probability of mistakenly concluding that u > action level and alpha (%), probability of mistakenly concluding that u < action level and examining the resulting changes in the number of samples. The following table shows the results of this analysis. Number of Samples AL=10 a-5 a=10 a=15 S=4.6 s=2.3 s=4.6 s=2.3 s=4.6 s=2.3 0=5 231 59 183 47 153 39 LBGR=90 Q=10 183 47 140 36 115 29 0=15 154 40 115 30 92 24 R=5 59 16 47 13 39 11 LBGR=80 R=10 47 13 36 10 29 8 0=15 40 11 30 8 24 7I,