6. (15) A new electrochemical method is used to determine the arsenic content in

Question

6. (15) A new electrochemical method is used to determine the arsenic content in an insecticide sample. The following results are obtained (as wt% As2O3): 1 1.19, 11.29, 11.27, 11.29, and 11.22 %. a) Calculate the mean value ofthe wt% As203 in the sample, the median, the range, the standard deviation, and the 95% confidence interval. (You can use a stats package in a calculator, or Excel, to calculate X and s; explicitly show the calculations of the other quantities.). b) Many analytical methods are susceptible to systematic errors. Briefly describe a way in which the presence of some type of possible systematic error in the new method could be detected. 2 7. (20) A supervisor in an environmental testing lab asks one of her staff to analyze for polychlorinated biphenyls (PCB's) in a sample, using a new type of chromatography column packing. The following results were obtained (in parts per billion): 249, 250, 255, 246, 247, and 253 ppb a) Calculate the mean value of the PCB concentration, the median, and the standard deviation (you ean usa a etats nacka 1n a calculator, or Excel, to calculate X and s

Explanation / Answer

Given wt% of As2o3 are 11.19, 11.29, 11.27, 11.29, 11.22

Mean (M)= 11.19 + 11.29 + 11.27 + 11.29 + 11.22 / 5 = 56.26 / 5 = 11.25

Range = Highest value - lowest value = 11.29 - 11.19 = .10

Arranging in ascending order we get 11.19, 11.22, 11.27, 11.29, 11.29

Median = Middle most value in the data = 11.27

Standard deviation (s) = (xi - xmean)2 / (n-1) = 0.17977 / (5-1) = 0.04494

The formula for confidence interval estimation is: = M ± Z(sM)

where M = sample mean
Z = Z statistic determined by confidence level
sM = standard error = (s2/n)

For 95% confidence interval z= 1.96

M = 11.25
t = 1.96
sM = (0.044942/5) = 0.02

= M ± Z(sM)
= 11.25 ± 1.96*0.02
= 11.25 ± 0.0394

M = 11.25, 95% CI [11.2106, 11.2894]

You can be 95% confident that the population mean () falls between 11.2106 and 11.2894.

Minimising systematic error

Systematic error is difficult to identify and correct. Given a particular experimental procedure and setup, it doesn't matter how many times you repeat the experiment and averages your measurements; the error remains unchanged. No statistical analysis of the data set will eliminate a systematic error, or even alert you to its presence. Systematic error can be located and minimized with a very careful analysis and design of test conditions and procedure; by comparing your results to other results obtained independently, using different equipment or techniques; or by following an experimental procedure on a known reference value, and adjusting the procedure until we obtain the desired result.

Check that any equations or computer programs you are trying to use to process data behave in the way you have expected. Sometimes it is good to try a program out on a set of values for which the correct results are known beforehand.

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