1. The problem statement, all variables and given/known data The life in hours of a battery is known to be normally distributed, with standard deviation of 1.5 hours. A random sample of 12 batteries has a sample mean life time of 50 hours. a) Test the hypothesis that the mean battery life is 50.5 hours (by using α = 0.05). b) What is the P-value for the test in part (a)? c) Find the β-error for the test in part (a). d) What sample size is required to ensure that beta does not exceed 0.10, if the true mean life is 52 hours? The solution is included as TheSolution.jpg. 2. Relevant equations z = (Xbar - μ)/( σ √(N) ), where Xbar is sample mean, σ is the population standard deviation and N is the sample size. 3. The attempt at a solution I'm struggling a lot with this topic, and the fact that the solutions aren't very descriptive makes it harder to learn. I'm confused for even basic stuff. For example, What's the final answer to part (a)? Is the null hypothesis rejected because 87.49% < 95%? Also, I'm confused about one or two alpha tails, and I have no idea if this problem has one or two of them, or if it's just not related to this topic. Basically, how do I know the accuracy rate is 95% and not 90%? Also, for part (b), I don't see why 2*(1 - 0.8749) is being computed. I don't see anything about part (c). Where is the β value? As for part (d), could someone explain what the solution is doing? Any input would be GREATLY appreciated!