(a) Is there evidence to support the claim that mean battery life exceeds 4 hours? Use α = 0.05. (b) What is the P-value for the test in part (a)? (c) Compute the power of the test if the true mean battery life is 4.5 hours. (d) What sample size would be required to detect a true mean battery life of 4.5 hours if you wanted the power of the test to be at least 0.9? (e) Explain how the question in part (a) could be answered by constructing a one-sided confidence bound on the mean life.