Refer to Exercises 7.137 and 7.138.
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: x̅ = 3.1 ppm, s = .5 ppm.
a. Suppose an a-value of .05 is used to conduct the test. Does this change favor halting production? Explain.
b. Determine the value of β 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?