30 By law. an industrial plant can discharge no more than 500 gallons of waste water per hour, on the average, into a neighbonng 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 four hours are selected over a penod of a week. A computer printout shows the results: Variable WASTE Number of Cases 4 Mean SD 1000.0 400.0 SE of Mean 200.0

a) Test the null hypothesis that the mean discharge equals 500 gallons per hour against the alternative that the limit is being exceeded. Find the P-value, and interpret

b) Explain why the result of this test may be invalid, or at least very highly approximate. if the population distribution of discharge is far from normal.

c) Explain how your one-sided analysis implicitly tests the broader null hypothesis that 500

d) Make a decision, using = 05 Interpret.

e) If the decision in

(d) was incorrect, what type of error was made? What could you do 10 reduce the chance of that type of error?