iid 3. Let X1,.,Xn 100(1 a)-th percentile of the standard normal distribution. N(0,02), 00 <...

   

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iid 3. Let X1,.,Xn 100(1 – a)-th percentile of the standard normal distribution. N(0,02), 00 < 0 < xo, o2 > 0. Assume o? is known. Denote za as the Is there a Uniformly Most Powerful critical region for testing Ho 0<1 versus Hị : 0 > 1 ? Why or why not? Suppose that you want to test Ho : 0 = 1 versus H1 : 0 + 1. Assume that you set the size of the test to be a = 0.05. What test will you use? Show that this test leads to the critical region {(x1, ., x16) : 4(ī – 1) > k}, where k is determined by a = 0.05. For the test in (g), recall that under the null hypothesis Ho : 0 = 1, A N (0, 1) and ( -x?(1). Explain when you would reject Ho. Use the fact that P( |< 1.96) = 0.95 to construct a 95% confidence interval for 0. Interpret this confidence interval. iid 3. Let X1,.,Xn 100(1 – a)-th percentile of the standard normal distribution. N(0,02), 00 < 0 < xo, o2 > 0. Assume o? is known. Denote za as the Is there a Uniformly Most Powerful critical region for testing Ho 0<1 versus Hị : 0 > 1 ? Why or why not? Suppose that you want to test Ho : 0 = 1 versus H1 : 0 + 1. Assume that you set the size of the test to be a = 0.05. What test will you use? Show that this test leads to the critical region {(x1, ., x16) : 4(ī – 1) > k}, where k is determined by a = 0.05. For the test in (g), recall that under the null hypothesis Ho : 0 = 1, A N (0, 1) and ( -x?(1). Explain when you would reject Ho. Use the fact that P( |< 1.96) = 0.95 to construct a 95% confidence interval for 0. Interpret this confidence interval.

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