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statsquiz6 - Quiz 6 Probability and Statistics Bernardo...

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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 ² . 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 0 : ° = ² , H 1 : ° > ² (b) H 0 : ° = ² , H 1 : ° ² ² (c) H 0 : ° = ² , H 1 : ° 6 = ² (d) H 0 : ° > ² , H 1 : ° ± ² (e) H 0 : ° > ² , H 1 : ° = ² 2. I need to choose the level of signi°cance ³ . About ³ , it is true that: a type 2 error. a type 2 error, but the power of the test also decreases.
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