Fluoride in drinking water. Many water treatment facilities supplement the natural fluoride concentration with hydrofluosilicic acid in order to reach a target concentration of fluoride in drinking water. Certain levels are thought to enhance dental health, but very high concentrations can be dangerous. Suppose that one such treatment plant targets .75 milligram per liter (mg/L) for their water. The plant tests 25 samples each day to determine whether the median level differs from the target.

a. Set up the null and alternative hypotheses.

b. Set up the test statistic and rejection region using a = .10.

c. Explain the implication of a Type I error and a Type II error in the context of this application.

d. Suppose that one day’s samples result in 18 values that exceed .75 mg/L. Conduct the test and state the appropriate conclusion in the context of this application.

e. When it was suggested to the plant’s supervisor that a t-test should be used to conduct the daily test, she replied that the probability distribution of the fluoride concentrations was “heavily skewed to the right.” Show graphically what she meant by this and explain why this is a reason to prefer the sign test to the t-test.