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7.21 Refer to Exercise 7.13. Suppose that n = 20 observations are to be taken on In(LC50) mea- surements and that o² = 1.4. Let S² denote the sample variance of the 20 measurements. a b c Find a number b such that P(S² ≤ b) = .975. Find a number a such that P(a ≤ S²) = .975. If a and b are as in parts (a) and (b), what is P(a ≤ S² ≤ b)?

7.21 Refer to Exercise 7.13. Suppose that n = 20 observations are to be taken on In(LC50) mea- surements and that o² = 1.4. Let S² denote the sample variance of the 20 measurements. a b c Find a number b such that P(S² ≤ b) = .975. Find a number a such that P(a ≤ S²) = .975. If a and b are as in parts (a) and (b), what is P(a ≤ S² ≤ b)?

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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7.21 Refer to Exercise 7.13. Suppose that n = 20 observations are to be taken on In(LC50) mea- surements and that o² = 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 ≤ $²) = .975. c If a and b are as in parts (a) and (b), what is P(a ≤ S² ≤ b)?
Transcribed Image Text:7.21 Refer to Exercise 7.13. Suppose that n = 20 observations are to be taken on In(LC50) mea- surements and that o² = 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 ≤ $²) = .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 normally distributed, and, hence, the analysis is based on In(LC50) data. Studies of the effects of copper on a certain species of fish (say, species A) show the variance of In(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 In(LC50) will differ from the true population mean by no more than .5.
Transcribed Image Text: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 normally distributed, and, hence, the analysis is based on In(LC50) data. Studies of the effects of copper on a certain species of fish (say, species A) show the variance of In(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 In(LC50) will differ from the true population mean by no more than .5.
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