Homework Assignment - Chapter 4 - Fall 2011

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1 Homework - Chapter 4 - Fall 2011 On differences between the 7th and 8th edition: In 4-A in the 7th edition, you are asked to perform a Q test instead of a Grubbs test; the former is no longer discussed in the 8th edition, and I am not sure if any comment is made on the reason for this. As a result, we will not discuss the use of the Q test, nor make reference to it in future problems. For part (d) of 4-F, the equations used in Harris in the 8th edition are different fro those of the 7th edition; stick to the 8th edition equations, which are given below. For 4-E and 4-G, just use an Excel spreadsheet. If you want to use your calculator or do a manual calculation (as for an exam), please do so. Exercises 4-A. For the numbers 116.0, 97.9, 114.2, 106.8, and 108.3, find the mean, standard deviation, range, and 90% confidence interval for the mean. Using the Grubbs test, decide whether the number 97.9 should be discarded. 4-B. Spreadsheet for standard deviation. Let s create a spreadsheet to compute the mean and standard deviation of a column of numbers in two different ways. The spreadsheet here is a template for this exercise. 1

2 (a) Reproduce the template on your spreadsheet. Cells B4 to B8 contain the data (x values) whose mean and standard deviation we will compute. (b) Write a formula in cell B9 to compute the sum of numbers in B4 to B8. (c) Write a formula in cell B10 to compute the mean value. (d) Write a formula in cell C4 to compute (x mean), where x is in cell B4 and the mean is in cell B10. Use Fill Down to compute values in cells C5 to C8. (e) Write a formula in cell D4 to compute the square of the value in cell C4. Use Fill Down to compute values in cells D5 to D8. (f) Write a formula in cell D9 to compute the sum of the numbers in cells D4 to D8. (g) Write a formula in cell B11 to compute the standard deviation. (h) (i) (j) (k) Use cells B13 to B18 to document your formulas. Now we are going to simplify life by using formulas built into the spreadsheet. In cell B21 type =SUM(B4:B8), which means find the sum of numbers in cells B4 to B8. Cell B21 should display the same number as cell B9. In general, you will not know what functions are available and how to write them. In Excel 2007, use the Formulas ribbon and Insert Function to find SUM. In earlier versions of Excel, find the Function menu under Insert. Select cell B22. Go to Insert Function and find AVERAGE. When you type =AVERAGE(B4:B8) in cell B22, its value should be the same as B10. For cell B23, find the standard deviation function ( =STDEV(B4:B8) ) and check that the value agrees with cell B11. 4-C. Use Table 4-1 for this exercise. This exercise and 4-D deal with picking areas from a Gaussian curve, manually (4-C) and using Gaussian (4-D). Suppose that the mileage at which sets of automobile brakes had been 80% worn through was recorded. The average was , and the standard deviation was miles. (a) What fraction of brakes is expected to be 80% worn in less than miles? (b) What fraction is expected to be 80% worn at a mileage between and miles? 4-D. Use the NORMDIST spreadsheet function in Excel to answer these questions about the brakes described in Exercise 4-C: (a) What fraction of brakes is expected to be 80% worn in less than miles? (b) What fraction is expected to be 80% worn at a mileage between and miles? 4-E. A reliable assay shows that the ATP (adenosine triphosphate) content of a certain cell type is 111 µmol/100 ml. You developed a new assay, which gave the following values for replicate analyses: 117, 119, 111, 115, 120 µmol/100 ml (average = 116.4). Does your result agree with the known value at the 95% confidence level? Note: You may calculate the standard deviation by hand, or much more quickly with an Excel spreadsheet. Look up the t-value in Table 4.2 (Student s t-test values); also, try using the Excel function TINV (where format is TINV(probability, degrees of freedom), in this calculation, TINV (0.95,4)). 2

3 4-F. Traces of toxic, man-made hexachlorohexanes in North Sea sediments were extracted by a known process and by two new procedures, and measured by chromatography. (a) Are the concentrations parts per million, parts per billion, or something else? (b) Is the standard deviation for procedure B significantly different from that of the conventional procedure? Use the F test to make this determination. (c) Is the mean concentration found by procedure B significantly different from that of the conventional procedure? (d) Answer the same two questions as parts (b) and (c) to compare procedure A to the conventional procedure. Note, if the F-test finds that there is a significant difference between the standard deviations at a particular confidence level, then the spooled equation is not applicable, and one must use: and tcalc is obtained from Please note that the 7th edition uses quite different equations than these; please stick to these ones, as they give the proper answers. 3

4 4-G. Calibration curve. (You can do this exercise with your calculator, but it is more easily done using the Excel spreadsheet - see Chapter 4 notes for an example). In the Bradford protein determination, the color of a dye changes from brown to blue when it binds to protein. Absorbance of light is measured. (a) (b) (c) Find the equation of the least-squares straight line through these points in the form y = [m(±sm)]x + [b(±sb)] with a reasonable number of significant figures. Make a graph showing he experimental data and the calculated straight line. An unknown protein sample gave an absorbance of Calculate the number of micrograms of protein in the unknown and estimate its uncertainty. 4

5 Problems Gaussian distribution Easy 4-1, 4-2, 4-3 Excel problem 4-5 Confidence Intervals, t Test, F test, and Grubbs Test Easy 4-8, 4-10, 4-11, 4-12, 4-14* Intermediate and Excel 4-17 (4-16, 7th) 4-18 (4-17, 7th), 4-23*, 4-24 (4-23 7th), 4-25 (4-24 7th), 4-31, 4-35 *absent from 7th edition, so listed below. P4-14. The CdSe content (g/l) of nanocrystals was measured by two methods for six different samples. Do the two methods differ significantly at the 95% confidence level? P4-23. Should the value 216 be rejected from the set of results 192, 216, 202, 195, and 204? 5