2011-11-04美国地质学会年会布劳斯专题讨论会_苏树春关于美国环保总署块状石棉鉴定的论文.pptVIP

November 4, 2012 * of 40 Shu-Chun Su: M 435 Equation for Calculating Sample Size where n – sample size that is large enough to attain the specified maximum allowed error and confidence level p – a rough estimate of population proportion (B%) E – MAE (maximum allowed error) z – critical value from normal distribution corresponding to the specified confidence level z = 1.96 for 95% confidence level z = 2.575 for 99% confidence level Nate: 1. Given z and p, this equation can be used to calculate the margin of error associated with a specific n 2. The derivation of this equation is omitted in this presentation, which can be found in general probability/statistics texts November 4, 2012 * of 40 Shu-Chun Su: M 435 Sample Size (Points to Be Counted) to Attain Specified MAE and CL at Different p For example, if asbestos% is 0.25% and the margin of error is set at 0.10%, at minimum 9,580 points are to be counted to attain 95% CL. In other words, if the sample is repeatedly analyzed 100 times it is expected that the resulted asbestos% is within 0.15% - 0.35% 95 times November 4, 2012 * of 40 Shu-Chun Su: M 435 How Many Point Should be Counted ? Assuming Amphibole particles and non-asbestos particles are perfect spheres with the same diameter and density The sample is ideally homogeneous The amphibole concentration level is approx. 0.25 wt% Confidence level CL is set at 95% At minimum 1,533 points will have to be counted to ensure the resulted Amphibole wt% is accurate within ±0.25% At minimum 9,580 points will have to be counted to ensure the resulted Amphibole wt% is accurate within ±0.10% At minimum 38,320 points will have to be counted to ensure the resulted Amphibole wt% is accurate within ±0.05% November 4, 2012 * of 40 Shu-Chun Su: M 435 Another Use of the Sample Size Table Given the points counted and the measured asbestos%, the margin of error can be calculated for a specified CL for different p as follows: For example, if 400 points are counted