The life in hours of a battery is known to be approximately normally distributed, with standard deviation hours. A random sample of 10 batteries has a mean life of hours. (a) Is there evidence to support the claim that battery life exceeds 40 hours? Use . The battery life Choose your answer in accordance to the item a) of the question statement significantly different greater than 40 hours at . (b) What is the P-value for the test in part (a)? P-value = Enter your answer in accordance to the item b) of the question statement Round your answer to three decimal places (e. g. 98.765). (c) What is the β-error for the test in part (a) if the true mean life is 42 hours? β = Enter your answer in accordance to the item c) of the question statement Round your answer to five decimal places (e. g. 98.76543). (d) What sample size would be required to ensure that β does not exceed 0.2 if the true mean life is 44 hours?