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98 Continued from page 97
Modern Analytical Chemistry

Experiments Spencer, R. D. “The Dependence of Strength in Plastics upon The absorbance of solutions of food dyes is used to explore

the treatment of outliers and the application of the t-test for
Polymer Chain Length and Chain Orientation,” J. Chem.
Educ. 1984, 61, 555–563.
comparing means.
The stretching properties of polymers are investigated by
Vitha, M. F.; Carr, P. W. “A Laboratory Exercise in Statistical
examining the effect of polymer orientation, polymer chain
Analysis of Data,” J. Chem. Educ. 1997, 74, 998–1000.
length, stretching rate, and temperature. Homogeneity of
Students determine the average weight of vitamin E pills using
polymer films and consistency between lots of polymer films
several different methods (one at a time, in sets of ten pills,
also are investigated. Statistical analysis of data includes Q-
and in sets of 100 pills). The data collected by the class are
tests and t-tests.
pooled together, plotted as histograms, and compared with
Thomasson, K.; Lofthus-Merschman, S.; Humbert, M.; et al. results predicted by a normal distribution. The histograms and
“Applying Statistics in the Undergraduate Chemistry standard deviations for the pooled data also show the effect of
Laboratory: Experiments with Food Dyes,” J. Chem. Educ. sample size on the standard error of the mean.
1998, 75, 231–233.

4K PROBLEMS

1. The following masses were recorded for 12 different U.S. (a) For each dosage, calculate the mean and standard
quarters (all given in grams): deviation for the milligrams of morphine hydrochloride per
–
tablet. (b) Assuming that X and s are good approximations
2
5.683 5.549 5.548 5.552
2
for mand s , and that the population is normally distributed,
5.620 5.536 5.539 5.684
what percentage of tablets at each dosage level are expected to
5.551 5.552 5.554 5.632 contain more than the nominal amount of morphine
Report the mean, median, range, standard deviation, and hydrochloride per tablet?
variance for these data. 4. Daskalakis and co-workers recently evaluated several
2. Shown in the following rows are results for the determination procedures for digesting the tissues of oysters and mussels
of acetaminophen (in milligrams) in ten separate tablets of prior to analyzing the samples for silver. One of the
20
Excedrin Extra Strength Pain Reliever. 18 methods used to evaluate the procedure is a spike
recovery in which a known amount of silver is added
224.3 240.4 246.3 239.4 253.1
to the tissue sample and the percent of the added silver
261.7 229.4 255.5 235.5 249.7
found on analysis is reported. Ideally, spike recoveries
(a) Report the mean, median, range, standard deviation, and should fall within the range 100 ± 15%. The results
–
variance for these data. (b) Assuming that X and s are good for one method are
2
2
approximations for mand s , and that the population is
normally distributed, what percentage of tablets are expected 106% 108% 92% 99% 104% 101% 93% 93%
to contain more than the standard amount of 250 mg Assuming that the spike recoveries are normally distributed,
acetaminophen per tablet? what is the probability that any single spike recovery will be
3. Salem and Galan have developed a new method for within the accepted range?
determining the amount of morphine hydrochloride in 5. The formula weight (FW) of a gas can be determined using
tablets. Results, in milligrams, for several tablets containing the following form of the ideal gas law
19
different nominal dosages follow gRT
FW =
100-mg 60-mg 30-mg 10-mg PV
tablets tablets tablets tablets
where g is the mass in grams, R is the gas constant, T is the
99.17 54.21 28.51 19.06 temperature in kelvins, P is the pressure in atmospheres, and
94.31 55.62 26.25 8.83 V is the volume in liters. In a typical analysis the following
95.92 57.40 25.92 9.08 data are obtained (with estimated uncertainties in
94.55 57.51 28.62 parentheses)
93.83 52.59 24.93