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Unformatted text preview: Quiz 6 Probability and Statistics Bernardo Guimaraes September 2009 (For questions 1 to 10) A random sample of size n is drawn from X & N ( &; 2 ) . Denote an element of the sample by X i ; 1 i n . I want to test whether the expected value of X is bigger than . De&ne & X = P n i =1 X i n . Denote by the cdf of a normally distributed variable with mean 0 and variance 1. 1. The null and alternative hypothesis to be tested are: (a) H : & = , H 1 : & > (b) H : & = , H 1 : & (c) H : & = , H 1 : & 6 = (d) H : & > , H 1 : & (e) H : & > , H 1 : & = 2. I need to choose the level of signi&cance . About , it is true that: (a) The best thing to do is to pick a very high , so the power of the test is high. (b) The best thing to do is to pick a very low , so the power of the test is high. (c) needs to be around 0.05, which corresponds to the zone of reasonable doubt. (d) The lower is , the lower is the probability of a type I error but the higher is the probability of a type 2 error. (e) The lower is , the lower is the probability of a type I error and the lower is the probability of a type 2 error, but the power of the test also decreases....
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This note was uploaded on 02/28/2010 for the course ECO 211 taught by Professor Gilo during the Spring '10 term at Young Harris.
- Spring '10