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4-40. Benzene is a toxic ing of medicinal chemicals, dyes, artificial leather, and linoleum. A manufacturer claims that its exit water meets the federal regulation with a mean of less than 7980 ppm of ben- zene. To assess the benzene content of the exit water, 10 independent water samples were collected and found to have an average of 7906 ppm of benzene. Assume a known stan- dard deviation of 80 ppm and use a significance level of 0.01. (a) Test the manufacturer's claim. Use the P-value approach. (b) What is the ß-value if the true mean is 7920? (c) What sample size would be necessary to detect a true mean of 7920 with a probability of at least 0.90?

4-40. Benzene is a toxic ing of medicinal chemicals, dyes, artificial leather, and linoleum. A manufacturer claims that its exit water meets the federal regulation with a mean of less than 7980 ppm of ben- zene. To assess the benzene content of the exit water, 10 independent water samples were collected and found to have an average of 7906 ppm of benzene. Assume a known stan- dard deviation of 80 ppm and use a significance level of 0.01. (a) Test the manufacturer's claim. Use the P-value approach. (b) What is the ß-value if the true mean is 7920? (c) What sample size would be necessary to detect a true mean of 7920 with a probability of at least 0.90?

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 1GP
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4-40. Benzene is a toxic chemical used in the manufactur- ing of medicinal chemicals, dyes, artificial leather, and linoleum. A manufacturer claims that its exit water meets the federal regulation with a mean of less than 7980 ppm of ben- zene. To assess the benzene content of the exit water, 10 independent water samples were collected and found to have an average of 7906 ppm of benzene. Assume a known stan- dard deviation of 80 ppm and use a significance level of 0.01. (a) Test the manufacturer's claim. Use the P-value approach. (b) What is the ß-value if the true mean is 7920? (c) What sample size would be necessary to detect a true mean of 7920 with a probability of at least 0.90? (d) Find a 99% one-sided upper confidence bound on the true mean. (e) Use the CI found in part (d) to test the hypothesis.
Transcribed Image Text:4-40. Benzene is a toxic chemical used in the manufactur- ing of medicinal chemicals, dyes, artificial leather, and linoleum. A manufacturer claims that its exit water meets the federal regulation with a mean of less than 7980 ppm of ben- zene. To assess the benzene content of the exit water, 10 independent water samples were collected and found to have an average of 7906 ppm of benzene. Assume a known stan- dard deviation of 80 ppm and use a significance level of 0.01. (a) Test the manufacturer's claim. Use the P-value approach. (b) What is the ß-value if the true mean is 7920? (c) What sample size would be necessary to detect a true mean of 7920 with a probability of at least 0.90? (d) Find a 99% one-sided upper confidence bound on the true mean. (e) Use the CI found in part (d) to test the hypothesis.
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