Stat 312: Lecture 13 Two-sample tests Moo K. Chung [email protected]March 6, 2003 Concepts 1. The P-value is the smallest level of signiFcance at which H0 would be rejected. P-value ≤ α → reject H0 at level α . P-value > α → do not reject H0 at level α . The smaller the P-value, the easier to reject H0 . 2. Let X 1 , ··· , X n and Y 1 , ··· , Y m be two indepen-dent samples with mean μ X , μ Y and variance σ 2 X , σ 2 Y respectively. Assume n and m to be large . The test statistic for testing H0 : μ X = μ Y vs. H 1 : μ X 6 = μ Y Z = ¯ Y-¯ X q σ 2 X /n + σ 2 Y /m ∼ N (0 , 1) . 3. Let X 1 , ··· , X n and Y 1 , ··· , Y m be two inde-pendent samples with X i ∼ N ( μ X , σ 2 X ) and Y j ∼ N ( μ Y , σ 2 Y ). Then we can show that Z = ¯ Y-¯ X q σ 2 X /n + σ 2 Y /m ∼ N (0 , 1) . In-class problems Example 8.11. 47 out of 102 doctors did not know the generic name for the drug methadone. Let p be the proportion of doctors who knew the generic name. Determine the
This is the end of the preview. Sign up
access the rest of the document.
This note was uploaded on 01/31/2008 for the course STAT 312 taught by Professor Chung during the Spring '04 term at University of Wisconsin.