Question: 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, 2009). A major plastic manufacture, 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: x?=3.1, s=.5.

a) (5 points) Do these statistics provide sufficient evidence to halt the production process? Use α=.01.

b) (3 points) In the context part a), define a Type II error.

c) (3 points) Calculate β for the test in part a) assuming that the true mean is μ=3.1 ppm.

d) (2 points) 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?

e) (2 points) Repeat parts c) and d) 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?