Question: Regulations require that your factory provide convincing evidence that it discharges less than 25 milligrams of a certain pollutant each week, on average, over the long run. A recent sample shows weekly amounts of 13, 12, 10, 8, 22, 14, 10, 15, 9, 10, 6, and 12 milligrams released.
a. Have you complied with the regulations? Explain your answer based on a one-sided hypothesis test at the 5% level.
b. Report the p-value as either p > 0.05, p < 0.05, p < 0.01, p < 0.001.
c. Identify the underlying hypotheses and assumptions involved in these tests.
d. All else equal, would the use of a two-sided test, instead of a one-sided test, result in more or fewer instances of "out-of-compliance" findings? Explain.