Probability and Statistics for Engineering and the Sciences (with CD-ROM and InfoTrac )

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Stat 312: Lecture 12 Errors in hypothesis testing Moo K. Chung [email protected] Oct 20, 2004 Type I error : you reject H 0 when H 0 is true. P ( Type I error ) = P ( reject H 0 | H 0 true ) = α. The resulting α is called the significance level of the test and the corresponding test is called a level α test . We will use test procedures that give α less than a specified level (0.05 or 0.01 usually). I believe that dogs are as smart as people. Assume IQ of a dog follows X i N ( μ, 10 2 ) . IQ of 10 dogs are measured: 30, 25, 70, 110, 40, 80, 50, 60, 100, 60. We want to test if dogs are as smart as people by testing H 0 : μ = 100 vs. H 1 : μ < 100 . (1) Let ¯ X be a test statistic and R = ( -∞ , 90) to be a rejection region. Let’s compute the probabil- ity of making Type I error based on this testing procedure. Under the assumption H 0 is true, X i N (100 , 10 2 ) . Under this condition, ¯ X N (100 , 10) and α = P ( ¯ X < 90) . >help(pnorm)
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This note was uploaded on 01/31/2008 for the course STAT 312 taught by Professor Chung during the Fall '04 term at University of Wisconsin.

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lecture12 notes - Stat 312 Lecture 12 Errors in hypothesis...

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