6.8. By law, an industrial plant can discharge no more than 500 gallons of waste 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 a random sample of four hours is selected over a period of a week. Software reports:

Variable No. Cases Mean SD SE of Mean WASTE 4 1000.0 400.0 200.0

(a) Test whether the mean discharge equals 500 gallons per hour against the alternative that the limit is being exceeded. Find the P-valuc and interpret.

(b) Explain why the test may be highly approximate or even invalid if the population distribution of discharge is far from normal.

(c) Explain how your one-sided analysisimplicitly tests the broader null hypothesis thatix < 500.