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EPA limits vinyl chloride (cont’d). Refer to Exercise
Chapter 7, Problem 136SE(choose chapter or problem)
Problem 136SE
EPA limits vinyl chloride (cont’d). Refer to Exercise 7.135.
a. In the context of the problem, define a Type II error.
b. Calculate for the test described in part a of Exercise 7.135, assuming that the true mean is = 3.1 ppm.
c. What is the power of the test to detect a departure from the manufacturer’s 3.0 ppm limit when the mean is 3.1 ppm?
d. Repeat parts b and c assuming that the true mean is 3.2 ppm. What happens to the power of the test as the plant’s mean vinyl chloride level departs further from the limit?
Questions & Answers
QUESTION:
Problem 136SE
EPA limits vinyl chloride (cont’d). Refer to Exercise 7.135.
a. In the context of the problem, define a Type II error.
b. Calculate for the test described in part a of Exercise 7.135, assuming that the true mean is = 3.1 ppm.
c. What is the power of the test to detect a departure from the manufacturer’s 3.0 ppm limit when the mean is 3.1 ppm?
d. Repeat parts b and c assuming that the true mean is 3.2 ppm. What happens to the power of the test as the plant’s mean vinyl chloride level departs further from the limit?
ANSWER:
Solution:
Step 1 of 4:
From the data of EPA limits on vinyl chloride
We have = 3.1ppm, s = 0.5 ppm, and n = 50
- The claim is to define Type II error for the problem.
A Type II error would be concluding the mean amount of vinyl chloride in the air is less than or equal to 3 parts per million when, in fact, it is more than 3 parts per million.