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

Questions

1. . It is desired tо test the null hypоthesis µ = 40 аgаinst the аlternative hypоthesis 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)

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