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122 Analytical Chemistry 2.0obtaining results of 0.080 756 659 and 0.991 802 464. Subtract the smallervalue from the larger value and adjust to the correct number of significantfigures to arrive at a probability of 0.9910, or 99.10%.Excel also includes a function for binomial distributions. The function’sformat is=binomdist(X, N, p, T/F)where X is the number of times a particular outcome occurs in N trials, andp is the probability of X occurring in one trial. Setting the function’s lastterm to TRUE gives the total probability for any result up to X and settingit to FALSE to give the probability for X. Using Example 4.10 to test thisfunction, we find that the probability of finding no atoms of 13 C atoms ina molecule of cholesterol, C 27 H 44 O) using the formula=binomdist(0, 27, 0.0111, FALSE)which returns a value of 0.740 as an answer, after adjusting the significantfigures. Using the formula=binomdist(2, 27, 0.0111, TRUE)we find that 99.7% of cholesterol molecules contain two or fewer atomsof 13 C.A B C1 Set 1 Set 22 3.080 3.0523 3.094 3.1414 3.107 3.0835 3.056 3.0836 3.112 3.0487 3.1748 3.198Figure 4.21 Portion of a spreadsheet containingthe data in Table 4.11.Significance Te s t sExcel’s Analysis ToolPak includes tools to help you complete the followingsignificance tests covered in this chapter:• an F-test of variances• an unpaired t-test of sample means assuming equal variances• an unpaired t-test of sample means assuming unequal variances• a paired t-test for of sample meansLet’s use the ToolPak to complete a t-test on the data in Table 4.11, whichcontains results for two experiments to determine the mass of a circulatingU. S. penny. Enter the data from Table 4.11 into a spreadsheet as shownin Figure 4.21. Because the data in this case are unpaired, we will useExcel to complete an unpaired t-test. Before we can complete a t-test wemust use an F-test to determine whether the variances for the two data setsare equal or unequal. Our null hypothesis is that the variances are equal,2 2s = s , and our alternative hypothesis is that the variances are notSet1 Set22 2equal, s ≠ s .Set1 Set2To complete the F-test select Data Analysis... from the Tools menu,which opens a window entitled “Data Analysis.” Scroll through the window,select F-Test Two Sample Variance from the available options, and clickOK. Place the cursor in the box for the “Variable 1 range” and then clickand drag over the cells B1:B8. Next, place the cursor in the box for “Variable2 range” and then click and drag over the cells B1:B6. Check the box
Chapter 4 Evaluating Analytical Data123F-Test Two-Sample for VariancesData Set 1 Data Set 2Mean 3.11728571 3.0814Variance 0.00259224 0.0013843Observations 7 5df 6 4F 1.87259849P(F
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Detailed Table of ContentsPreface..
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4C.4 Uncertainty for Mixed Operatio
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13. Kinetic Methods .. . . . . . .
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