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: \(\overline x = 3.1\)ppm,\(s = 0.5\)ppm.

a. Do these statistics provide sufficient evidence to halt the production process? Use\(\alpha = 0.01\).

b. If you were the plant manager, would you want to use a large or a small value for\(\alpha \)the test in part a? Explain.

c. Find the p-value for the test and interpret its value

Short answer

The null and the alternative hypotheses are \({H_0}:\mu = 3.0\)and \({H_a}:\mu > 3.0\)

Step-by-step solution

Given information

The information is regarding a significant plastics manufacturer attempting to control the amount of vinyl chloride its workers are exposed.

A random sample of 50 air specimens produced the following statistics

\(\overline x = 3.1\)ppm

\(s = 0.5\)ppm

Concept of the null and the alternative hypothesis

The alternative hypothesis of a test expresses your research’s prediction of an effect or relationship. In contrast, the null hypothesis of a test always predicts no effect or no association between variables.

Setting up the null and the alternative hypothesis

a.

The claim is that the mean amount of vinyl chloride in the air exceeds 3.0 ppm.

From the given information, the null and the alternative hypotheses are

Null hypothesis:

\({H_0}:\mu = 3.0\)

The mean amount of vinyl chloride in the air is 3.0 ppm

Alternative hypothesis:

\({H_a}:\mu > 3.0\)

The mean amount of vinyl chloride in the air is more significant than 3.0 ppm