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Data File C:Oocumenis and SettingslsmahinilMy Docu Variable: Xylenes(mg/kg) <br /> r <br /> Raw Statistics Norma[Distribution Test <br /> Number of Valid Samples 10 Shapiro-Wilk Test Statisitic . 0.512295 <br /> Number of Unique Samples 8 Shapiro-Wslk 5%Critical Value 0.842 <br /> Minimum 0.0025 Data not normal at 5%significance level d <br /> Maximum 950 <br /> Mean 130.5939 95%UCL(Assuming Normal Distribution) <br /> Median 0.02 Student's-t UCL 309.2098 <br /> Standard Deviation 308.1276 <br /> Variance 94942.76 Gamma.Distribution Test <br /> a <br /> i- Coefficient of Vadnticc 2.359435 A Tcst Statistic - 1.325285 <br />( Skewness 2.578929 A-D 5%Critical Value 0.880539 R <br /> K-S Test Statistic 0.335514 <br /> Gamma Statistics K-S 5%Critical Value 0.297476 <br /> k hat 0.122119 Data do not follow gamma distribution <br /> k star(bias corrected) 0.15215 at 5%significance level <br /> Theta hat 1069"403 <br /> Theta star 858.3253 95%UCLs(Assuming Gamma Distribution) <br /> t <br /> no hat 2.442371: Approximate Gar;ma UCL !031.962 <br /> nu star 3.042993 Adjusted Gamma UCL 1503.925 r <br /> Approx"Chi Square Value(.05) 0.385068 <br /> j Adjusted Level of Significance 0.0267 Lognormal Distribution Test <br /> Adjusted Chi Square Value 0.26424 Shapiro-Wilk Test Statisitic 0.620425 <br /> Shapiro-Wilk 5%Critical Value 0.842 <br /> q Log-transformed Statistics Data not lognormal at 5%significance level ' <br /> j Minimum of log data -5.991465 ' <br />{ Maximum of log data 6.856462 95%UCLs(Assuming Lognormal Distribution) <br /> � Mean of log data -1.606408 95%H.-UCL 5.16E412 <br /> Standard Deviation of log data 4.762706 95%Chebyshev(MVUE)11CL 801.0404 <br /> Variance of log data 22.68337 97.5%Chebyshev(MVUE)UCL 1081.808 <br /> 99%Chebyshev(MVUE)UCL 1633.322 <br /> 95%Non-parametric UCLs <br /> CLT UCL 290.8661 <br /> Adj-CLT UCL(Adjusted for skewness) 375.7745 <br /> I Mod-t UCL(Adjusted for skewness) 322.4538 <br /> Jackknife UCL - 309.2098 <br /> Standard Bootstrap UCLO'-'iJ 9 <br /> Bootstrap-t UCL 22452.23 <br /> RECOMMENDATION Hall's Bootstrap UCL 25722.28 <br /> Data arc`'cn-,parametric(0.05) - Pcrccn;i€e Leots:rap UCL 320AO55 <br /> 8CA f3ootstrap UCL 390,0056 <br /> Use Hall's Bootstrap UCL 95%Chebyshev(Mean,Sd)UCL 555.3188 <br /> 97.5%Chebyshev(Mean,Sd)UCL 739.0976 <br /> Recommended UCL exceeds the maximum[ 99%Chebyshev(Mean,Sd)UCL 1100.095 <br /> In case Hall's Bootstrap method yields <br /> an erratic,unrea"sonabty large UCL value. <br /> I <br /> use 99%Chebyshev(Mean,Sd)UCL i <br /> 1 <br /> i <br />( I <br /> i <br /> a ' <br /> I <br /> F <br /> I <br />