A manager of a campus store that sells posters conjectures that more than 30% of all freshman dorm rooms have a poster of a rock group. From n = 60 rooms selected at random, an investigator records X = number of rooms having a poster of a rock group. (a) Formulate a null and alternative hypotheses for verifying the conjecture.
(b) Select a rejection region for which a = .05.
(c) If p = .4, what error can be made? Explain in words in the context of the problem.
(d) What is the conclusion of your test if X = 25?
(e) Based on your conclusion in part (d), what error could you have made? Explain in the context of the problem.