Analytical Chem istry - DePauw University

142 Analytical Chemistry 2.0Many of the problems that follow require accessto statistical tables. For your convenience,here are hyperlinks to the appendices containingthese tables.Appendix 3: Single-Sided Normal DistributionAppendix 4: Critical Values for the t-TestAppendix 5: Critical Values for the F-TestAppendix 6: Critical Values for Dixon’s Q-TestAppendix 7: Critical Values for Grubb’s Test1.764 1.838 1.865 1.866 1.872 1.8771.890 1.891 1.891 1.897 1.899 1.9001.906 1.908 1.910 1.911 1.916 1.9191.920 1.922 1.927 1.931 1.935 1.9361.936 1.937 1.939 1.939 1.940 1.9411.941 1.942 1.943 1.948 1.953 1.9551.957 1.957 1.957 1.959 1.962 1.9631.963 1.963 1.966 1.968 1.969 1.9731.975 1.976 1.977 1.981 1.981 1.9881.993 1.993 1.995 1.995 1.995 2.0172.029 2.042(a) Calculate the mean and standard deviation for this data. (b)Construct a histogram for this data. From a visual inspection ofyour histogram, does the data appear to be normally distributed?(c) In a normally distributed population 68.26% of all members liewithin the range m ± 1s. What percentage of the data lies withinthe range ± 1s? Does this support your answer to the previous question?(d) Assuming that X and s 2 are good approximations for mand s 2 , what percentage of all experimentally determined Cu/Sratios will be greater than 2? How does this compare with the experimentaldata? Does this support your conclusion about whetherthe data is normally distributed? (e) It has been reported that thismethod of preparing copper sulfide results in a non-stoichiometriccompound with a Cu/S ratio of less than 2. Determine if the meanvalue for this data is significantly less than 2 at a significance levelof a = 0.01.32. Real-time quantitative PCR is an analytical method for determiningtrace amounts of DNA. During the analysis, each cycle doubles theamount of DNA. A probe species that fluoresces in the presence ofDNA is added to the reaction mixture and the increase in fluorescenceis monitored during the cycling. The cycle threshold, C t , is the cyclewhen the fluorescence exceeds a threshold value. The data in the followingtable shows C t values for three samples using real-time quantitativePCR. 30 Each sample was analyzed 18 times.Sample X Sample Y Sample Z24.24 25.14 24.41 28.06 22.97 23.4323.97 24.57 27.21 27.77 22.93 23.6624.44 24.49 27.02 28.74 22.95 28.7924.79 24.68 26.81 28.35 23.12 23.7730 Burns, M. J.; Nixon, G. J.; Foy, C. A.; Harris, N. BMC Biotechnol. 2005, 5:31 (open accesspublication).