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4 <br /> Data File G\Documents and SettingslsmahiniWy Docu Variable: MTBE in GW <br />` (N9rL) i; ! <br /> Raw Statistics Normal Distribution Test <br /> Number of Valid Samples 12 Shapiro-Wilk Test Statisitic , 0,660362 . <br /> Number of Unique Samples 5 Shapiro-Wilk 5%Critical Value 0.859 <br /> Minimum 0.25 Data not normal at 5%significance level <br /> Maximum 0.77' ° <br /> Mean 0.393333 95%UCL(Assuming Normal Distribution) <br /> Median 0.25 Student's-t UCL 0.508206 <br /> Standard Deviation 0.221578 <br /> Variance 0,049097. Gamma Distribution Test <br /> Coefficient of Variation 0.563335 A-D Test Statistic 2.104917 <br /> Skewness 1.067992 A-D 51/.Critical Value 0.735131 <br /> K-S Test Statistic 0.422189 <br /> Gamma Statistics K-S 5%Critical Value 0.246317 <br /> k hat 4.177646 Data do not follow gamma distribution <br /> k star(bias corrected) 3-18879 at 5%significance level <br /> Theta hat 0.094152 <br /> 1 Theta star 0.123349 95%UCLs(Assuming Gamma Distribution) <br /> 1 nu hat 100.2635 Approximate Gamma UCL 0.524645 <br /> nu star 76.53097 Adjusted Gamma UCL 0.548796 <br /> Approx.Chi Square Value(.05) 57.37623 - o' <br /> II Adjusted Level of Significance 0.02896 Lognormal Distribution Test <br /> Adjusted Chi Square Value 54.85135 Shapiro-Wilk Test Statisitic 0.65506 <br /> 'i Shapiro-Wilk 5%Critical Value 0.859 <br /> Log-transformed Statistics Data not lognormal at 5%significance level <br /> Minimum of log data -1.386294 5 <br />}! Maximum of log data -0.261365 95%UCLs(Assuming Lognormal Distribution) <br /> Mean of log data -1.057531 95%H-UCL 0,541235- <br /> Standard Deviation of log data 0.496862 95%Chebyshev(MVUE)UCL 0.637173 <br /> I Variance of log data 0.246892 97.5%Chebyshev(MVUE)UCL 0.744753 n <br /> 99%Chebyshev(MVUE)UCL 0.956072 <br /> Y <br /> 95%Non-parametric UCLs <br /> CLT UCL 0.498545 <br /> Adj-CLT UCL(Adjusted for skewness) 0.519616 <br /> Mod-t UCL(Adjusted for skewness) 0.511492 <br /> I Jackknife UCL ! 0.508206 <br /> Standard Bootstrap UCL ;n;G935+ <br /> Bootstrap-t UCL 0.545091 <br /> i RECOMMENDATION Hall's Bootstrap UCL 0.467715 <br /> 1 Data are Non-parametric(0.05) Percentile Bootstrap UCL == 0.500833 , <br /> BCA Bootstrap UCL 0.508333 <br /> Use Student's-t UCL 95%Chebyshev(Mean,Sd)UCL 0.672147 <br /> or Modified-t UCL 97.5%Chebyshev(Mean,Sd)UCL 0.792789 ' <br /> 99%Chebyshev(Mean,Sd)UCL 1:029769 <br /> IG <br /> 4 ,r, <br /> f <br /> { I <br /> 1 � <br /> J <br /> I <br /> { <br /> 1 <br /> r ' <br />