Medical researchers have developed the new artificial heart constructed primarily of titanium as well as plastic. The heart will last and operate almost indefinitely once it is implanted in patient's body, but the battery pack requires to be recharged about every four hours. A random sample of 50 battery packs is chosen and subjected to a life test. The average life of these batteries is 4.05 hours. Suppose that battery life is normally distributed with standard deviation s=0.2 hour. α = .05
What sample size would be required to detect true mean battery life of 4.5 hours if we wanted the power of test to be at least .9?