D. Harvey - Modern Analytical Chemistry (794078), страница 33
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Using X-ray diffraction, Karstang and Kvalheinreported a new method for determining the weightpercent of kalonite in complex clay minerals.27 To test themethod, nine samples containing known amounts ofkalonite were prepared and analyzed. The results (as%w/w kalonite) are shown.Actual: 5.0 10.0Found: 6.8 11.720.0 40.019.8 40.550.053.660.061.780.078.929. The following data were collected during a study of theconcentration of Zn in samples drawn from several locationsin Lake Erie (all concentrations in parts per million).Location[Zn2+] at theair–waterinterface[Zn2+] at thesediment–waterinterface1234560.4300.2660.5670.5310.7070.7160.4150.2380.3900.4100.6050.60990.0 95.091.7 94.7Evaluate the accuracy of the method at α = 0.05.27.
Mizutani and colleagues reported the development of a newmethod for the analysis of l-malate.28 As part of their studythey analyzed a series of beverages using both their methodand a standard spectrophotometric procedure based on aclinical kit purchased from Boerhinger Scientific. A summaryfollows of their results (in parts per million).SampleApple juice 1Apple juice 2Apple juice 3Apple juice 4Grape juice 1Grape juice 2Mixed fruit juice 1Mixed fruit juice 2White wine 1White wine 2White wine 3White wine 4ElectrodeSpectrophotometric34.022.629.724.917.814.88.631.410.817.315.718.433.428.429.524.818.315.48.531.911.517.615.418.3Determine whether there is a significant difference betweenthe methods at α = 0.05.28.
Alexiev and associates describe an improved photometricmethod for the determination of Fe3+ based on itscatalytic effect on the oxidation of sulphanilic acid byKIO4.29 As part of their study the concentration ofFe3+ in human serum samples was determined by theproposed method and the standard method.Following are the results, with concentrations inmicromoles/L.Sample12345678Proposed MethodStandard Method8.259.759.759.7510.7511.2513.8814.258.068.848.368.7313.1313.6513.8513.43Determine whether there is a significant difference betweenthe two methods at α = 0.05.Determine whether there is a significant difference betweenthe concentration of Zn2+ at the air–water interface and thesediment–water interface at α = 0.05.30.
Ten laboratories were asked to determine the concentrationof an analyte A in three standard test samples. Following arethe results, in parts per million.30Laboratory12345678910Sample 122.623.021.521.921.322.123.121.722.221.7Sample 2Sample 313.614.213.913.913.513.513.913.512.913.816.015.916.316.916.717.417.516.817.216.7Determine if there are any potential outliers in Sample 1,Sample 2, or Sample 3 at a significance level of α = 0.05.31. When copper metal and powdered sulfur are placed in acrucible and ignited, the product is a sulfide with an empiricalformula of CuxS.
The value of x can be determined byweighing the Cu and S before ignition, and finding the massof CuxS when the reaction is complete. Following are the Cu/Sratios from 62 such experiments.1.7641.8971.9201.9391.9571.9681.9931.8381.8991.9221.9401.9571.9691.9931.8651.9001.9271.9411.9571.9731.9951.8661.9061.9311.9411.9591.9751.9951.8721.9081.9351.9421.9621.9761.9951.8771.9101.9361.9431.9631.9772.0171.8901.9111.9361.9481.9631.9812.0291.8911.9161.9371.9531.9631.9812.0421.8911.9191.9391.9551.9661.988(a) Calculate the mean and standard deviation for these data.(b) Construct a histogram for this data set.
From a visualinspection of your histogram, do the data appear to benormally distributed? (c) In a normally distributedpopulation, 68.26% of all members lie within the rangeµ ± 1σ. What percentage of the data lies within the range–X ± 1s? Does this support your answer to the previous1400-CH04 9/8/99 3:55 PM Page 102102Modern Analytical Chemistry–question? (d) Assuming that X and σ2 are goodapproximations for µ and σ2, what percentage of allexperimentally determined Cu/S ratios will be greater than 2?How does this compare with the experimental data? Does thissupport your conclusion about whether the data are normallydistributed? (e) It has been reported that this method forpreparing copper sulfide results in a nonstoichiometriccompound with a Cu/S ratio of less than 2.
Determine if themean value for these data is significantly less than 2 at asignificance level of α = 0.01.4L SUGGESTED READINGSA more comprehensive discussion of the analysis of data, coveringall topics considered in this chapter as well as additional material,can be found in any textbook on statistics or data analysis;following are several such texts.Anderson, R. L. Practical Statistics for Analytical Chemists. VanNostrand Reinhold: New York, 1987.Graham, R. C. Data Analysis for the Chemical Sciences. VCHPublishers: New York, 1993.Mark, H.; Workman, J. Statistics in Spectroscopy. Academic Press:Boston, 1991.Mason, R.
L.; Gunst, R. F.; Hess, J. L. Statistical Design andAnalysis of Experiments. Wiley: New York, 1989.Miller, J. C.; Miller, J. N. Statistics for Analytical Chemistry, 3rd ed.Ellis Horwood PTR Prentice-Hall: New York, 1993.Sharaf, M. H.; Illman, D. L.; Kowalski, B. R. Chemometrics. WileyInterscience: New York, 1986.The difference between precision and accuracy and a discussion ofindeterminate and determinate sources of erroris covered in the following paper.Treptow, R.
S. “Precision and Accuracy in Measurements,”J. Chem. Educ. 1998, 75, 992–995.The detection of outliers, particularly when working with a smallnumber of samples, is discussed in the following papers.Efstathiou, C. “Stochastic Calculation of Critical Q-Test Values forthe Detection of Outliers in Measurements,” J. Chem. Educ.1992, 69, 773–736.Kelly, P. C.
“Outlier Detection in Collaborative Studies,” Anal.Chem. 1990, 73, 58–64.Mitschele, J. “Small Sample Statistics,” J. Chem. Educ. 1991, 68,470–473.The following papers provide additional information on error anduncertainty, including the propagation of uncertainty.Andraos, J. “On the Propagation of Statistical Errors for aFunction of Several Variables,” J. Chem. Educ. 1996, 73,150–154.Donato, H.; Metz, C. “A Direct Method for the Propagation ofError Using a Personal Computer Spreadsheet Program,”J.
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Chem. Educ. 1993, 70,776–779; Part 2. Some Worked Examples, J. Chem. Educ. 1993,70, 838–841.Heydorn, K. “Detecting Errors in Micro and Trace Analysis byUsing Statistics,” Anal. Chim. Acta 1993, 283, 494–499.Taylor, B. N.; Kuyatt, C. E. “Guidelines for Evaluating andExpressing the Uncertainty of NIST Measurement Results,”NIST Technical Note 1297, 1994.A further discussion of detection limits is found inCurrie, L. A., ed. Detection in Analytical Chemistry: Importance,Theory and Practice. American Chemical Society: Washington,DC, 1988.4M REFERENCES1. Goedhart, M. J.; Verdonk, A.
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