The supplier of a particular brand of vitamin pills claims that the average potency of these pills after a certain exposure to heat and humidity is at least 65. Before buying these pills, a distributor wants to verify the supplier's claim is valid. To this end, the distributor chooses a random sample of 9 pills from a batch and measures their potency after the specified exposure.
(a) Formulate the hypotheses about the mean potency p.
(b) Determine the rejection region of the test with α = .05. State any assumption you make about the population.
(c) The data are 63, 72, 64, 69, 59, 65, 66, 64, 65. Apply the test and state your conclusion.