In Example 4.3, the paper mill had to demonstrate that its effluent had mean DO greater than 6 mg/L. But to ensure against occasional very low DO, keeping the mean high is not enough, the mill must also keep the standard deviation low.
(a) Using the data in Table 4.3, is there evidence that the standard deviation is less than 0.5 mg/L? Use a significance level of 1%.
(b) The test used in (a) requires the data come from a normal distribution. Use a box plot and a normal probability plot to check this assumption.
Example 4.3
One-sided alternative hypotheses frequently occur in regulatory situations. Suppose, for example, that the state environmental protection agency requires a paper mill to aerate its effluent so that the mean dissolved oxygen (DO) level is demonstrably above 6 mg/L. To monitor compliance, the state samples water specimens at 12 randomly selected dates. The data is given in Table 4.3. In view of the critical role of DO, the agency is requiring very strong evidence that mean DO is high. Has the paper mill demonstrated compliance, if α is set at 1%?
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