The life in hours of a battery is known to be approximately normally distributed, with standard deviation σ=1.25 hours. a random sample of 10 batteries has a mean life of x¯=40.5 hours. (a) is there evidence to support the claim that battery life exceeds 40 hours? use α=0.050. (b) what is the p-value for the test in part () what is the β-error for the test in part (a) if the true mean life is 42 hours? (d) what sample size would be required to ensure that β does not exceed 0.1 if the true mean life is 44 hours? (e) round your answers to three significant digits.