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Examples for 09-01-2009 - STAT 420 Examples for Fall 2009 1...

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STAT 420 Examples for 09/01/2009 Fall 2009 1. Assume that the distributions of Y 1 and Y 2 are N ( μ 1 , σ 2 ) and N ( μ 2 , σ 2 ) , respectively. Given the n 1 = 6 observations of Y 1 , 65, 68, 67, 66, 71, 68 and the n 2 = 8 observations of Y 2 , 68, 70, 67, 71, 70, 72, 73, 69 test H 0 : μ 1 = μ 2 vs. H 1 : μ 1 μ 2 using the ANOVA F test. Use a 5% level of significance. What can you say about the p-value of this test? Recall: n 1 = 6, n 2 = 8, 1 y = 67.5, 2 y = 70, 2 1 s = 4.3, 2 2 s = 4, 2 pooled s = 4.125, H 0 : μ 1 = μ 2 t test statistic: t = – 2.279. t 0.025 ( 12 ) = 2.179. J = 2 . N = n 1 + n 2 = 6 + 8 = 14 . 14 965 14 70 8 5 . 67 6 ... 2 2 1 1 = = = + + + + N J J y n y n y n y = 68.92857 . SSB = ( ( ( 2 2 2 2 2 1 1 ... y y n y y n y y n J J - + + - + - = 6 ( 67.5 – 68.92857 ) 2 + 8 ( 70 – 68.92857 ) 2 = 21.42857 . MSB = 1 21.42857 1 SSB = - J = 21.42857 .
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SSW = ( ( ( 2 2 2 2 2 1 1 1 ... 1 1 J J s n s n s n - + + - + - = 5 4.3 + 7 4 = 49.5 . MSW = 12 49.5 SSW = - J N = 4.125 . [ = 2 pooled s ] SSTot = SSB + SSW = 70.92857 . F = 4.125 21.42857 MSW MSB = = 5.1948 . [ = t 2 ] ANOVA table: Source SS DF MS F Between 21.42857 1 21.42857 5.1948 Within 49.5 12 4.125 Total 70.92857 13 F 0.05 ( 1, 12 ) = 4.75 . [ = ( t 0.025 ( 12 ) ) 2 ] Reject
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