Quiz 8

Time:  20 minutes.  This quiz is open book, open notes.

1.    Samples of sediment in a river basin yielded values of 8, 8, 20, and 64 mg/Kg (ppm) arsenic.  To analyze the results, you will model all variation as random.  Specifically, these values will be considered as independent realizations of a random variable governed by one probability distribution.  Its mean characterizes the average arsenic concentration river-wide.

1. Estimate the mean and variance assuming the underlying distribution is Normal.  Use unbiased estimators (2 minutes).
2. Estimate the mean using the maximum likelihood estimator, assuming the underlying distribution is Lognormal (4 minutes).  

2.    Environmental scientists are concerned about sediments with more than 50 ppm arsenic in this river.

1. Estimate the proportion of sediments with more than 50 ppm arsenic.  Use the binomial distribution (15 seconds).
2. Use your answer to (1a) above to estimate the proportion of sediments with more than 50 ppm arsenic (1 minute).  

3.    (Extra credit)  Explain why each method in problem 2 gives a highly uncertain answer.

Notes

The natural logarithms of the data are 2, 2, 3, and 4.

Scoring: The passing score is 92.  You must show details of your work to get credit for a correct answer or partial credit for an incorrect answer.

Return to the Environmental Statistics home page

This page is copyright (c) 2001 Quantitative Decisions.  Please cite it as

This page was created 13 March 2001.