(Solved): 2/ Medical researchers have developed a new artificial heart constructed primarily of titanium an ...

2/

Medical researchers have developed a new artificial heart constructed primarily of titanium and plastic. The heart will last and operate almost indefinitely once it is implanted in the patient's body, but the battery pack needs to be recharged about every four hours. A random sample of 50 battery packs is selected and subjected to a life test. The average life of these batteries is \( 4.05 \) hours. Assume that battery life is normally distributed with standard deviation \( \sigma=0.2 \) hour. Use \( \alpha=0.05 \). (a) Is there evidence to support the claim that mean battery life exceeds 4 hours? (b) Compute the power of this test if the true mean battery life is \( 4.5 \) hours. Round your answer to two decimal places (e.g. 98.76). (c) What sample size would be required if we want to detect a true mean battery life of \( 4.5 \) hours if we wanted the power of the test to be at least \( 0.90 \) ?