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

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

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(a) Test whether 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 test may be highly approximate or even invalid if the population distribution of discharge is far from normal.

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