Math Stat Final-2009 - Mathematical Statistics-2009 Final...

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Mathematical Statistics-2009 6/25/2009 Final Exam 10:00-12:30 1. State the definitions of the following terms. (1) Type I error and type II error. (2) Power function and the relationship with (1) (3) Size of a test. (4) The most powerful size α test. (5)The likelihood ratio (LR) test. 2. Suppose that you are interested in conducting the statistical test of H : µ ൌ 255 vs H : µ ൐ 255 , and you have decided to use following decision rule: Reject H if the sample mean of a random sample of 81 items is more than 270. Assume that the population standard deviation is 63. (1) Find the probability of making a type I error. (2) Find the probability of making a type I error when µ ൌ 260 . What is the shape of the power function would you expect? Draw the picture and explain in words. 3. Let X ,X ,…,X be a random sample of size n. (1) State and prove the Neyman-Pearson (NP) Lemma. (2)
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This note was uploaded on 05/09/2011 for the course DIF 1486 taught by Professor Yow-jenjou during the Spring '11 term at National Chiao Tung University.

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