2011_SS1_Homework 06 - Solutions

00 2160 fail to reject null hypothesis if the sample

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Unformatted text preview: must first calculate the pooled estimate of the variance. First: SS + SS1 710 + 460 2 1170 s 2 ed = 1 , s 2 ed = , s pooled = , s 2 ed = 90 pool pool pool df1 + df2 8+5 13 Next, calculate the estimated standard error for the sample mean difference s12 = s( X1 ! X2 ) = s 2 ed pool n1 + s 2 ed pool n2 , s( X1 ! X2 ) = 90 90 + , s( X1 ! X2 ) = 10 + 15 , s( X1 ! X2 ) = 5 9 6 Estimated standard error of the mean difference = 5 Additionally, not on the homework but useful for your own knowledge: If the sample mean difference is 10 points, is this enough evidence to reject the null hypothesis using a two ­tailed test with ! = 0.05 ? ( X ! X2 ) 10 t( X1 ! X2 ) = 1 , t( X1 ! X2 ) = , t( X1 ! X2 ) = 2 s( X1 ! X2 ) 5 df = (n1 ­1)+(n2 ­1)=13, ! = 0.05 , t critical = ± 2.160 |tobserved| < |tcritical|, |2.00 | < |2.160|, Fail to Reject Null Hypothesis If the sample mean difference is 13 points, is this enough evidence to re...
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