Suppose X,..., Xn iid Uniform(0, 0), where > 0 is unknown. Consider testing Ho: 02 30...

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Suppose X₁,..., Xn iid Uniform(0, 0), where > 0 is unknown. Consider testing Ho: 02 30 versus H₁ : 0 < 30 Let T = max{X₁,..., Xn}. A test will reject Ho if T < c for some c> 0. (a) For each value c > 0, find the size a(c) of the test. (b) What's problematic about the following? "We should choose c≥ 30 for the rejection region, since when H₁ is true, we'll detect it with 100% probability." [Hint: consider (a).] = (c) If n 10, T25, find the p-value and use it to draw a conclusion for the test at the a = 0.10 level of significance. = 20 with at 0.01 test.]. (d) What is the smallest n such that a level a = 0.01 test detects least 80% probability? [Tip: first find the rejection region for a level a = (e) Find the smallest value n for a level a = 0.01 test that detects = 20 with 100% probability. Explain why the rejection region leads to 100% power at 0 = 20. Suppose X₁,..., Xn iid Uniform(0, 0), where > 0 is unknown. Consider testing Ho: 02 30 versus H₁ : 0 < 30 Let T = max{X₁,..., Xn}. A test will reject Ho if T < c for some c> 0. (a) For each value c > 0, find the size a(c) of the test. (b) What's problematic about the following? "We should choose c≥ 30 for the rejection region, since when H₁ is true, we'll detect it with 100% probability." [Hint: consider (a).] = (c) If n 10, T25, find the p-value and use it to draw a conclusion for the test at the a = 0.10 level of significance. = 20 with at 0.01 test.]. (d) What is the smallest n such that a level a = 0.01 test detects least 80% probability? [Tip: first find the rejection region for a level a = (e) Find the smallest value n for a level a = 0.01 test that detects = 20 with 100% probability. Explain why the rejection region leads to 100% power at 0 = 20.

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a For each value c 0 find the size ac of the test The size of the test is defined as the probability of rejecting the null hypothesis when the null hy... View the full answer