A Harris Interactive Poll for Tylenol PM indicated that 8% of American students

Question

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. 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? Which error, type I or type II, is more serious for college officials? Why? Which error, type I or type II, is more serious for students? Why?

Explanation / Answer

a) Here we consider

a null hypothesis H0 that proportion of students who missed a test because they overslept is 0.08

against

an alternative hypothesis Ha that the proportion is greater than 0.08.

A test of significance for single proportion is to be needed for college officials to prove that the new academic policy is causing fewer students to be late for exams.

b) Type I error implies that we reject the null hypothesis when the hypothesis is actually true

in this situation type I error will be - the null hypothesis that 8% of students missed a test due to oversleeping is true but it is still rejected which will be the fault of the officials and is serious for them.

c) Type II error implies that we accept the null hypothesis when the hypothesis is actually false

in this situation type II error will be - proportion of the number of students who who missed a test due to oversleeping is false infact there are more students who miss test due to oversleeping but it is accepted that the there are only 8% student who miss the testby the officials.Here, the students will have to suffer so this will be more serious for the students.

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