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.
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).
1. The percentiles of the lead results are reported as 0.21, 0.42, 0.80, 1.36, and 2.21 ug/L. Their logarithms are -1.56, -0.87, -0.22, 0.31, and 0.79, respectively. Sketch a normal probability plot of the logarithms. [One minute]
2. "Eyeball" the slope and intercept of the normal probability plot in #1 to estimate the standard deviation and mean of the logarithms, respectively. [One minute]
3. Write down formulas you could use to estimate the mean and standard deviation of the lead data using your answers to #2. You don't have to evaluate the formulas, but make sure they contain numbers only--no variables. [Two minutes]
4. 1007 subjects were tested for lead. Suppose the correct answers to #3 are a mean of 0.9 ug/L and standard deviation of 0.8 ug/L. Write down a formula for a lower 90% confidence limit of the mean. You don't have to evaluate it, but make sure it contains numbers only--no variables. [Two minutes]
5. Write down (in words, not formulas) what the answer to #4 means in terms of the blood lead concentrations in people. [One minute]
6. Extra credit (valid only after answering questions 1-5). Compute the answers to #3 and #4. Use your answer to #3 in the computation for #4.
7. Extra credit. What is the problem with using the original lead results in #1 and #2 to estimate the mean and standard deviation directly (rather than going through the logarithms), thereby avoiding the formulas in #3?
Scoring: The passing score is 85.
Note: Here is a part of the 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 27 March 2001.