This quiz tests your understanding of Normal-theory computations of confidence intervals and percentile estimates.
Time: 20 minutes. Open book, open notes.
On March 21, 2001, the Centers for Disease Control (CDC) issued the National Report on Human Exposure to Environmental Chemicals. This report summarizes measurements of 27 environmental chemicals in the blood and urine of thousands of human test subjects. It is already receiving a lot of press coverage. See, for example, the New York Times article at http://www.nytimes.com/aponline/national/AP-Chemical-Exposure.html.
The summary statistics are the number of subjects (N), the geometric mean (GM), and the 10th, 25th, 50th, 75th, and 90th percentiles. All measurements are in micrograms per liter (ug/L).
The report also provides 95% confidence intervals for the GM and the percentiles.
1. 1024 subjects were tested for mono-ethyl phthalate. The GM is 176 with a confidence interval from 132 to 220. The logarithms of these numbers are 4.88, 5.17, and 5.39, respectively. Assuming a Lognormal distribution, compute the standard deviation of the logarithms of the 1024 values. (For such a large number of subjects, Student's t distribution agrees with the Normal distribution to two decimal places for all percentiles between 1 and 99. Some values of the standard Normal CDF are shown below.)
2. The percentiles of the mono-ethyl phthalate results are reported as 27.7, 61.5, 171, 424, and 1160 ug/L. Their logarithms are 3.32, 4.12, 5.14, 6.05, and 7.06. Are these values consistent with your answer to question 1?
3. Extra credit. Demonstrate that the data are reasonably consistent with the assumption of lognormality made in question 1.
Scoring: The passing score is 90.
Note: Here is a part of he Normal CDF.
| Percentage point | 75% | 90% | 95% | 97.50% | 99% |
| Value | 0.67 | 1.28 | 1.65 | 1.96 | 2.33 |
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This page was created 22 March 2001.