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Suppose we have a random sample of size 50 from a N(μ,σ2) PDF. We wish to...

Suppose we have a random sample of size 50 from a N(μ,σ2) PDF. We wish to test H0: μ=10 versus H1: μ=10. The sample moments are x ̄ = 13.4508 and s2 = 65.8016. (a) Test the null hypothesis that σ2 = 64 versus a two-sided alternative. First, find the critical region and then give your decision. (b) (5 points) Find a 95% confidence interval for σ2? (c) (5 points) If you are worried about performing 2 statistical tests on the same data and that the overall type I error might not be 5%, how might you modify your approach?

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