The life in hours of a battery is known to be approximately normally distributed with standard deviation = 1.0 hours. A random sample of 12 batteries has a mean life of = 41 hours. (a) Is there evidence to support the claim that battery life exceeds 40.5 hours? Use = 0.05. (b) What is the P-value for the test in part (a)? (c) What is the -error for the test in part (a) if the true mean life is 41.5 hours? (d) What sample size would be required to ensure that does not exceed 0.05 if the true mean life is 43.5? (e) Explain how you could answer the question in part (a) by calculating an appropriate confidence bound on life.