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Quiz4 - 36-226 Summer 2010 Quiz 4 July 30 1 Indicate...

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36-226 Summer 2010 Quiz 4 July 30 1. Indicate whether the following are TRUE or FALSE. Write the entire word below each state- ment. Do not assume ANYTHING not written in the problem statement. (a) If I fail to reject the null hypothesis with α = 0 . 01 then I can reject the null with α = 0 . 05. FALSE (b) The p -value is the probability that the alternative hypothesis is true given the data I have seen. FALSE (c) If { X > 2 } is the rejection region for an MP test of the hypothesis H 0 : θ = 0 versus H a : θ = 3, then this is also the rejection region for a UMP test of the hypothesis H 0 : θ = 0 versus H a : θ > 0. TRUE (d) Let X N( μ, 1) . There is no UMP test for the hypothesis H 0 : μ = 0 versus H a : μ 6 = 0. TRUE (e) If I fail to reject the null hypothesis, then the p -value was greater than α . TRUE 2. Let X 1 , . . . , X n be i.i.d. U(0 , θ ). Show that the Pareto distribution with density
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