4. [10 points] Let X1,..., Xn ~ iid Unif(0, 0). We again wish to test Ho:...

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4. [10 points] Let X1,..., Xn ~ iid Unif(0, 0). We again wish to test Ho: 0 = 1 vs H : 01. (a) In a previous HW problem, we found a 100(1 - a)% asymptotic confidence interval using the MOM estimator. The interval we computed was given by the endpoints 2X za/22X/3n. Propose a test for these hypotheses based on this asymptotic interval. (b) Do you expect this test to be size a? Justify your choice in a sentence or two. (Continued on the next page) 4. [10 points] Let X1,..., Xn ~ iid Unif(0, 0). We again wish to test Ho: 0 = 1 vs H : 01. (a) In a previous HW problem, we found a 100(1 - a)% asymptotic confidence interval using the MOM estimator. The interval we computed was given by the endpoints 2X za/22X/3n. Propose a test for these hypotheses based on this asymptotic interval. (b) Do you expect this test to be size a? Justify your choice in a sentence or two. (Continued on the next page)