1.  . It is desired to test the null hypothesis µ = 40 again…

1.  . It is desired to test the null hypothesis µ = 40 against the alternative hypothesis µ > 40 on the basis of a random sample from a population with standard deviation 5.                        If the probability of a Type I error is to be 0.04 and the probability of Type II error is to be 0.06 for µ = 39, find the required size of the sample.    (4 points)      2.    A lighting company claims that their LED light bulbs have an average lifespan of at most 15,000 hours. To test this claim, a random sample of 15 bulbs is selected, and their lifespans are recorded. The sample mean is found to be 14,800 hours with a standard deviation of 500 hours. Conduct a hypothesis test at a significance level of 0.05 to determine if the claim is supported. What distribution are you using and why?    (6 points)