Solution Found!
EPA limits on vinyl chloride. The EPA sets an airborne
Chapter 7, Problem 135SE(choose chapter or problem)
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: \(\bar{x}=3.1\ ppm\), s = .5 ppm.
a. Do these statistics provide sufficient evidence to halt the production process? Use \(\alpha\ =\ .01.\)
b. If you were the plant manager, would you want to use a large or a small value for \(\alpha\) for the test in part a? Explain.
c. Find the p-value for the test and interpret its value.
Questions & Answers
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, 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: \(\bar{x}=3.1\ ppm\), s = .5 ppm.
a. Do these statistics provide sufficient evidence to halt the production process? Use \(\alpha\ =\ .01.\)
b. If you were the plant manager, would you want to use a large or a small value for \(\alpha\) for the test in part a? Explain.
c. Find the p-value for the test and interpret its value.
ANSWER:Step 1 of 3
From the data of EPA limits on vinyl chloride
We have \(\bar{x}=3.1\) ppm, s = 0.5 ppm, and n = 50
a) The claim is to check whether these statistics provide sufficient evidence to halt the production process.
Instructions to halt production if the mean amount of vinyl chloride in the air exceeds 3.0 ppm.
The hypothesis is
\(\begin{array}{l}
H_{0}: \mu=3 \\
H_{1}: \mu>3 .
\end{array}\)
The test statistic is
\(\begin{aligned}
\mathrm{z} & =\frac{\bar{x}-\mu_{0}}{\frac{\sigma}{\sqrt{n}}} \\
& =\frac{3.1-3}{\frac{0.5}{\sqrt{50}}} \\
& =\frac{0.1}{0.0707} \\
& =1.4144
\end{aligned}\)
Where, \(\alpha=0.01\) then, \(z_{0.01}=2.33\) (from area under normal curve)
The calculated value is less than table value.
Hence, do not reject the null hypothesis.