Suppose the EPA was suing a large manufacturing company for not meeting federal emissions guidelines

Suppose the EPA was suing a large manufacturing company for not meeting federal emissions guidelines. Specifically, the EPA is claiming that the mean amount of sulfur dioxide in the air is dangerously high, higher than 0.09 parts per million. The EPA randomly took eight samples this past month around the company and obtained the following:

.0889 .0786 .0991 .0887 .0900 .0560 .0678 .0909

(a.) State the null and alternative hypotheses for this test situation.

Ho:
Ha:

(b) Perform the test of significance with alpha = .05.

(c) State your conclusion.

Solution:

a) The hypotheses are

b) From the sample, we get the following information:

We are going to use the t-statistics:

The critical t-value for, left-tailed, 7 degrees of freedom -1.985

c) This means that we failed to reject the null hypothesis. In other words, there's no evidence that indicates that the company is not beyond the legal limit.

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