Analytical Chem istry - DePauw University

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124 Analytical Chemistry 2.0dt-Test: Two-Sample Assuming Equal VariancesData Set 1 Data Set 2Mean 3.11728571 3.0814Variance 0.00259224 0.0013843Observations 7 5Pooled Variance 0.00210906Hypothesized Mean Difference 0df 10t Stat 1.33450508P(T
Chapter 4 Evaluating Analytical Data125Table 4.20 R Functions for Descriptive StatisticsParameterR Functionmeanmean(object)medianmedian(object)sample standard deviation sd(object)population standard deviation sd(object)*((length(object)-1)/length(object))^0.5sample variancevar(object)population variancevar(object)*((length(object)-1)/length(object))rangemax(object)-min(object)Pr o b a b i l i t y DistributionsIn Example 4.11 we showed that 91.10% of a manufacturer’s analgesictables contain between 243 and 262 mg of aspirin. We obtained this resultby calculating the deviation, z, of each limit from the population’s expectedmean, m, of 250 mg in terms of the population’s expected standard deviation, s, of 5 mg. After calculating values for z, we used the table in Appendix3 to find the area under the normal distribution curve between thetwo limits.We can complete this calculation in R using the function pnorm. Thefunction’s general format ispnorm(x, m, s)where x is the limit of interest, m is the distribution’s expected mean and sis the distribution’s expected standard deviation. The function returns theprobability of obtaining a result of less than x (Figure 4.24). Here is theoutput of an R session for solving Example 4.11.> pnorm(243,250,5)[1] 0.08075666> pnorm(262,250,5)[1] 0.9918025Subtracting the smaller value from the larger value and adjusting to thecorrect number of significant figures gives the probability as 0.9910, or99.10%.R also includes functions for binomial distributions. To find the probabilityof obtaining a particular outcome, X, in N trials we use the dbinomfunction.dbinom(X, N, p)where p is the probability of X occurring in one trial. Using Example 4.10to test this function, we find that the probability of finding no atoms of13 C atoms in a molecule of cholesterol, C 27 H 44 O) isFigure 4.24 Shown in blue is thearea returned by the functionpnorm(x, m, s)x
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(a)(b)Phase 2Phase 12.95 3.00 3.05
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Detailed Table of ContentsPreface..
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4C.4 Uncertainty for Mixed Operatio
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8B.1 Theory and Practice . . . . .
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13. Kinetic Methods .. . . . . . .
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Appendix 5: Critical Values for the
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