Question: #30. By law, an industrial plant can discharge no more than 500 gallons of wate water per hour, on the average into a neighboring lake. Based on other infractions they have noticed an environmental action group believes this limit is being exceeded. Monitoring the plant is expensive and only a small sample is possible. A random sample of 4 hours are selected over a period of a week:

n = 4

Mean = 1000

SD = 400

SE of the mean = 200

(a) Test the null hypothesis that the mean discharge equals 500 gallons per hour against the alternative that the limit is being exceeded.

(b) Explain how the result of this test may be invalid.

(c) Explain how your one-sided analysis implicitly tests the broader bull hypothesis that \(\mu \le 500\).

(d) Make a decision using \(\alpha =0.05\).

(e) If the decision in (d) was incorrect, what type of error was made?. What could you do to reduce the chance of that type of error?