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This is a paired comparison questionenter image description here:

The answer is: enter image description here

However, this is my thought of using a t test on difference of population means

enter image description here

$t=\frac{583.125 - 415 - 0}{\sqrt{\frac{262.5900866^2}{8}+\frac{261.5721698^2}{8}}}$

$t= 1.2829$

enter image description here

$df=13.99978881$

critital value $t_{0.05}(df=14)$= 1.76131

$1.2829 < 1.76131$

therefore no difference between the mean daily sales from the two stores. Why am I getting a different conclusion? Is it reasonable to think about it this way?

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    yes better suited for the $p$aired test, $p$ossible with u$n$paired but $n$ot a powerful test, use paired2012-10-05

1 Answers 1

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You are using the formula for the unpaired two sample t test. The paired t test is like a one-sample test of the null hypothesis that the paired difference is 0 vs alternative that it is different from 0. The test statistic and the degrees of freedom are different. It is a more appropriate and more powerful test when the pairs are positively correlated. I have discussed this in posts on CV.

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    CV is short for Cross Validation. It is an SE site where statisticians, machine learning/data mining expert2012-10-04