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

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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 significance at which H 0 would be rejected. P -value α reject H 0 at level α . P -value > α do not reject H 0 at level α . The smaller the P -value, the easier to reject H 0 . 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 H 0 : 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 P -values for testing H 0 : p = 0 . 5 , vs H 1 : p < 0 . 5 > p<-47/102 > (p-0.5)/sqrt(0.5*0.5/102) [1] -0.792118 > pnorm(-0.79) [1] 0.2147639
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