Question

- Studies have shown that people who work with benzene longer
than five years have 20 times the incidence of leukemia than the
general population. As a result, OSHA has set a time-weighted
average permissible exposure limit of 1 ppm. A steel manufacturing
plant, which exposes its workers to benzene daily, is under
investigation for possible violations of the permissible exposure
limit. Thirty-six measurements, taken over a period of 5 months,
yielded
*x**=2.1 ppm, s=4.1 ppm*Use this information to answer the following questions.- Define the parameter of interest in words and notation.
- State the null and alternative hypotheses in proper notation if the investigators are looking for evidence that the permissible exposure limit has been exceeded.
- Calculate the test statistic for these data. Provide this statistic in proper notation.
- Report the p-value for your calculated test statistic using the appropriate function in R.
- (5 points) Provide a conclusion for this study at the 1%
significance level. In context of the problem. Be sure to include
**all**parts of the conclusion as discussed in class.

Answer #1

Part a

The parameter of interest is given as population average permissible exposure limit.

Notation: µ = 1 ppm

Part b

The null and alternative hypotheses are given as below:

Null hypothesis: H_{0}: The permissible exposure limit
is 1 ppm.

Alternative hypothesis: H_{a}: The permissible exposure
limit is greater than 1 ppm.

H_{0}: µ = 1 versus H_{a}: µ > 1

This is an upper tailed test.

Part c

The test statistic formula is given as below:

t = (Xbar - µ)/[S/sqrt(n)]

We are given

Xbar = 2.1

S = 4.1

n = 36

df = n – 1 = 35

t = (2.1 – 1)/[4.1/sqrt(36)]

t = 1.6098

Test statistic = t = 1.6098

Part d

We have t = 1.6098

df = 35

So, p-value by using t-table is given as below:

P-value = 0.0582

Part e

We are given

P-value = 0.0582

α = 0.01

P-value > α = 0.01

So, we do not reject the null hypothesis

There is insufficient evidence to conclude that permissible exposure limit has been exceeded.

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