A Harris Interactive Poll for Tylenol PM indicated that 8% of American students have missed a test because they overslept. Suppose officials at a state college decide to apply a new academic policy regarding exams. If a student arrives late for a test, then the student receives a 0 for the test and cannot take a make-up test at a later time.
a. What hypotheses should be tested, in terms of p, the true proportion of students who have missed a test because they overslept, in order for college officials to prove that the new academic policy is causing fewer students to be late for exams?
b. Which error, type I or type II, is more serious for college officials? Why?
c. Which error, type I or type II, is more serious for students? Why?
Recently, researchers have speculated that eating a moderate amount of dark chocolate may increase the level of antioxidants, compounds that protect us against free radicals, which can cause heart disease and cancer. A study was designed, and the antioxidant concentration in patients who ate dark chocolate regularly was measured. This information was used to test the hypotheses
where m is the true mean percentage of antioxidants in the bloodstream.
a. Describe a type I error and a type II error in this context.
b. The Hershey Company, maker of Hershey’s chocolates, is very interested in the results of this study. Which error is more serious for this company? Why?