Stat 312: Lecture 13 Two-sample tests Moo K. Chung email@example.com 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
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