Question: Bacteria counts in a plant's liquid waste discharge. Suppose you manage a plant that purifies its liquid waste and dis- charges the water into a local river. An EPA inspector has collected water specimens of the discharge of your plant and also water specimens in the river upstream from your plant. Each water specimen is divided into five parts, the bacteria count is read on each, and the median count for each speci- men is reported. The bacteria counts for each of six specimens are reported in the following table for the two locations; the data are saved in the BACTERIA file.

1. Why might the bacteria counts shown here tend to be approximately normally distributed?
2. What are the appropriate null and alternative hypothe- ses to test whether the mean bacteria count for the plant
   discharge exceeds that for the upstream location? Be sure to define any symbols you use.
3. Conduct the test, part b. Carefully interpret the results.
4. What assumptions are necessary to ensure the validity of this test?

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