Refer to Exercise 7.13. Suppose that n = 20 observations are to be taken on ln(LC50) measurements and that σ2 = 1.4. Let S2 denote the sample variance of the 20 measurements.
- a Find a number b such that P(S2 ≤ b) = .975.
- b Find a number a such that P(a ≤ S2) = .975.
- c If a and b are as in parts (a) and (b), what is P(a ≤ S2 ≤ b)?
7.13 The Environmental Protection Agency is concerned with the problem of setting criteria for the amounts of certain toxic chemicals to be allowed in freshwater lakes and rivers. A common measure of toxicity for any pollutant is the concentration of the pollutant that will kill half of the test species in a given amount of time (usually 96 hours for fish species). This measure is called LC50 (lethal concentration killing 50% of the test species). In many studies, the values contained in the natural logarithm of LC50 measurements are
Studies of the effects of copper on a certain species of fish (say. species A) show the variance of ln(LC50) measurements to be around .4 with concentration measurements in milligrams per liter. If n = 10 studies on LC50 for copper are to be completed, find the probability that the sample mean of ln(LC50) will differ from the true population mean by no more than .5.
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Chapter 7 Solutions
Mathematical Statistics with Applications
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw Hill
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