Statistical Data Analysis Verified Test Bank Granger Ch.22

­­Chapter 22

Problem 22.1: Using the same data set we examined in the activity “Using Microsoft Excel to Generate a Mean and Standard Deviation,” use the statistical functions on your calculator to determine the mean and the standard deviation of the data set. You may need to review the owner’s manual or visit the manufacturer’s website for instructions on statistical functions on your calculator.

Problem 22.2: Use Excel or a similar spreadsheet program to determine the mean and standard deviation of the following data sample. Repeat the analysis using your calculator’s statistical functions.

Problem 22.3: Use Excel or a similar spreadsheet program to determine the mean and standard deviation of the following data sample. Repeat the analysis using your calculator’s statistical functions.

Problem 22.4: In your own words, explain how changing N and changing σ affect the histogram generated in the Activity “Random Number Generation and Plotting a Histogram in Microsoft Excel.”

Problem 22.5: For the data set used in the activity “Using Microsoft Excel to Calculate Confidence Limits,” determine the 90% and the 99% CL.

Problem 22.6: For the data set used in the activity “Using Microsoft Excel to Calculate Confidence Limits,” determine the 95% CL using Equation 22.8 and compare your answer to your answer from the activity.

Problem 22.7: Assume that you measured the mass of 1.0014 grams of potassium oxalate (K₂C₂O₄) on a digital balance and placed it in a one-liter volumetric flask with a rated precision of 0.001 L. Calculate the molarity of the final solution and report the molarity with a 95% CL using the appropriate propagation of error equation.

Problem 22.8: Use the data in Table 22.3 and determine the value (in ppm) cup 5 would have to be before Equation 22.10 would identify it as an outlier. Show your work.

Problem 22.9: Imagine that this set of five replicate data points were collected for the analysis of lead in drinking water.

(a) Calculate a mean, standard deviation, and 95% CL using this data set (you may want to use a spreadsheet).

(b) Perform a Q-test on the data set. How does the performance of a Q-test alter your answer in part (a)?

Problem 22.10: Perform a Grubbs’ test using the data set in Problem 22.9. Report the mean, standard deviation, and the 95% CL based on the results of the test.

Problem 22.11: You have just measured the pH of the water sampled from a local lake. You have ten replicate measurements with two different pH probes. The data are presented below. Conduct an F-test on the data set and comment on the results.

Problem 22.12: In 2006, the Anne Arundel County Maryland Department of Health tested local wells for elevated levels of arsenic. They found that 35 out of 71 wells showed elevated levels. Atomic absorption spectroscopy is a very convenient way to measure arsenic in water. Imagine you are a laboratory manager and you have given identical arsenic samples to two different technicians. Conduct an F-test on the two sets of data and comment on the results.

Problem 22.13: Use Equation 22.14 to calculate SS_y–y for the example given in the Activity “Letting Excel Perform LINEST to Give Linear Regression Data” (Spreadsheet 22.4).

Problem 22.14: Repeat Problem 22.13, but use a slope that is 1% lower and an intercept that is 1% higher than that seen in Spreadsheet 22.4. Compare the SSy–y you calculate with that found in 22.13. Is the result as expected? Explain.

Problem 22.15: The following data were obtained for a set of calibration solutions of p-nitroaniline, measured by absorbance using ultraviolet-visible spectrophotometry.

A p-nitroaniline solution of unknown concentration exhibited an average absorbance of 0.181 for five replicate samples. Assuming that the y-intercept is zero for the calibration, calculate the concentration of the unknown solution and the standard deviation in the calculation.

Problem 22.16: Repeat Problem 22.15, but do not assume that the intercept is zero for the calibration. Which set of results do you believe are more accurate? Explain. What additional information would you need in order to make a more definitive judgment?

Problem 22.17: The following data were obtained for the calibration of a flame atomic absorption instrument in the measurement of calcium:

CONCENTRATION OF Ca (ppm) ABSORBANCE (AU)

0.100 0.010

0.250 0.024

0.500 0.069

1.000 0.093

2.500 0.225

5.000 0.427

7.500 0.628

10.00 0.804

A urine sample was treated to remove interferences, resulting in a dilution factor of 5:2 of the original urine. The mean absorbance for calcium of three replicates of the diluted urine sample was found to be 0.325. Assuming that the intercept is zero for the calcium calibration, calculate the concentration of calcium in the original (undiluted) urine solution. Include a calculation of the standard deviation of your analysis.

Problem 22.18: Demonstrate that Equations 22.21 and 22.22 can be derived from Equations 22.17 and 22.18.

Problem 22.19: Demonstrate that the units of LODx (and thus LOQx) are concentration units. Assume that the concentration is in units of molarity and that the measurements are made in milliamps from an arbitrary detector.

Problem 22.20: In the experiment represented in Problem 22.17, eight blank measurements (AU) were made: 0.001, 0.000, 0.000, 0.001, 0.002, –0.001, 0.000, and –0.001. Calculate the LODy , LOQ y, LODx, and LOQ x.

Problem 22.21: Consider your results from Problem 22.19* and the data presented in Problem 22.17. If you were presenting these data for publication, would you need to redo the calculations you did in Problem 22.17? Explain.

Problem 22.22: Estimate LODx and LOQx for the data given in Spreadsheet 22.4.

Problem 22.23: Estimate LODx and LOQx for the data given in Problem 22.15 (zero intercept).

Problem 22.24: The calibration depicted in Figures 22.14 and 22.15 was created from the following data. Calculate the LOQx and estimate the LDR.

EXERCISE 22.1: In your own words, define the statistical terms population and sample.

EXERCISE 22.2: In your own words, define the statistical terms gross error, systematic error, and random error.

EXERCISE 22.3: In your own words, define and give equations for the statistical terms mean, standard deviation, variance, standard error, and CL.

EXERCISE 22.4: Input the following data set into a spreadsheet and use the spreadsheet to determine the mean, standard deviation, and the 95% CL of the data set.

EXERCISE 22.5: Plot the results of Problem 22.15 as a column graph with standard error bars. Repeat the exercise using standard deviation error bars.

EXERCISE 22.6: Using the statistical functions on your calculator, input the data set from Problem 22.17 and determine the mean, standard deviation, and the 95% CL of the data set.

EXERCISE 22.7: Input the following data set into a spreadsheet and perform a Q-test and a Grubbs’ test on the data set. Report the “best” mean, standard deviation, and the 95% CL of the data set.

EXERCISE 22.8: Plot the results of Problem 22.7 as a column graph with standard error bars. Repeat the exercise using standard deviation error bars.

EXERCISE 22.9: Input the following data set into a spreadsheet and perform a Q-test and a Grubbs’ test on the data set. Report the “best” mean, standard deviation, and the 95% CL of the data set.

EXERCISE 22.10: Plot the results of Problem 22.9 as a column graph with standard error bars. Repeat the exercise using standard deviation error bars.

EXERCISE 22.11: Water samples were sent to two different laboratories and analyzed for ppb mercury. Each laboratory conducted 10 replicate analyses. Perform an F-test on the data and comment on the results.

EXERCISE 22.12: Describe the relationships between accuracy and precision with respect to the concepts of systematic error and random error.

EXERCISE 22.13: Use Equation 22.14 to calculate SS_y–y for the example given in Problem 22.15.

EXERCISE 22.14: Estimate LODx and LOQx for the data given in Problem 22.15 with a nonzero intercept.

EXERCISE 22.15: Estimate LODy and LODx for the data given in Problem 22.24 (zero intercept).

EXERCISE 22.16: Open a spreadsheet and create a number string from 1 to 5,000. Program the spreadsheet to generate and graph npf with a mean of 2,500 and a standard deviation of 500. Properly label your graph and insert it into the spreadsheet. Print the spreadsheet and turn it in.

EXERCISE 22.17: Using the membrane filtration method, a sample of water from a local lake was sent to two different laboratories for a coliform bacteria analysis. Each laboratory tested five replicates and reported total coliform colony counts. The data are presented. Perform an analysis of the data, including a Grubbs’ test and an F-test. Comment on the data and report the results of the analysis.

EXERCISE 22.18: You have just standardized a batch of NaOH by titration against phthalic acid (MW 166.14 g/ mol). The phthalic acid standard was made by dissolving 2.0312 ± 0.0001g of phthalic acid into a 500 ± 0.2 mL volumetric flask. A burette was used to deliver 27.51 ± 0.02 ml of phthalic acid into 250 ± 0.2 mL of NaOH solution. Being mindful to propagate error through your calculations, determine the molarity and ±σ of the NaOH solution.

EXERCISE 22.19: Using the membrane filtration method, a sample of water from a local lake was sent to five different laboratories for a coliform bacteria analysis. Each laboratory tested five replicates and reported total coliform colony counts. The data are presented. Perform an analysis of the data, including a Grubbs’ test and an ANOVA. Comment on the data and report the results of the analysis.