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EPA limits on vinyl chloride (cont’d). Refer to Exercises
Chapter 7, Problem 137SE(choose chapter or problem)
Problem 137SE
EPA limits on vinyl chloride (cont’d). Refer to Exercises 7.135 and 7.136.
a. Suppose an α value of .05 is used to conduct the test. Does this change favor halting production? Explain.
b. Determine the value of b and the power for the test when α = .05 and µ = 3.1.
c. What happens to the power of the test when α is increased?
7.135 EPA limits on vinyl chloride. The EPA sets an airborne limit of 5 parts per million (ppm) on vinyl chloride, a colorless gas used to make plastics, adhesives, and other chemicals. It is both a carcinogen and a mutagen (New Jersey Department of Health, Hazardous Substance Fact Sheet, 2010). A major plastics manufacturer, attempting to control the amount of vinyl chloride its workers are exposed to, has given instructions to halt production if the mean amount of vinyl chloride in the air exceeds 3.0 ppm. A random sample of 50 air specimens produced the following statistics: = 3.1 ppm, s = .5 ppm.
a. Do these statistics provide sufficient evidence to halt the production process? Use α = .01.
b. If you were the plant manager, would you want to use a large or a small value for α for the test in part a? Explain.
c. Find the p-value for the test and interpret its value.
* 7.136 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 b for the test described in part a of Exercise 7.135, assuming that the true mean is µ = 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 137SE
EPA limits on vinyl chloride (cont’d). Refer to Exercises 7.135 and 7.136.
a. Suppose an α value of .05 is used to conduct the test. Does this change favor halting production? Explain.
b. Determine the value of b and the power for the test when α = .05 and µ = 3.1.
c. What happens to the power of the test when α is increased?
7.135 EPA limits on vinyl chloride. The EPA sets an airborne limit of 5 parts per million (ppm) on vinyl chloride, a colorless gas used to make plastics, adhesives, and other chemicals. It is both a carcinogen and a mutagen (New Jersey Department of Health, Hazardous Substance Fact Sheet, 2010). A major plastics manufacturer, attempting to control the amount of vinyl chloride its workers are exposed to, has given instructions to halt production if the mean amount of vinyl chloride in the air exceeds 3.0 ppm. A random sample of 50 air specimens produced the following statistics: = 3.1 ppm, s = .5 ppm.
a. Do these statistics provide sufficient evidence to halt the production process? Use α = .01.
b. If you were the plant manager, would you want to use a large or a small value for α for the test in part a? Explain.
c. Find the p-value for the test and interpret its value.
* 7.136 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 b for the test described in part a of Exercise 7.135, assuming that the true mean is µ = 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 3:
From exercise 7.135, we have n = 50, and s = 0.5 ppm.
a). We have to explain an is used to conduct the test, does this change favor halting production.
No, it increase the risk of falsely rejecting
That is closing the plant unnecessarily.