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- https://stats.libretexts.org/Courses/Fresno_City_College/Book%3A_Business_Statistics_Customized_(OpenStax)/10%3A_Hypothesis_Testing_with_Two_Samples/10.07%3A_Matched_or_Paired_SamplesEither the matched pairs have differences that come from a population that is normal or the number of differences is sufficiently large so that distribution of the sample mean of differences is approx...Either the matched pairs have differences that come from a population that is normal or the number of differences is sufficiently large so that distribution of the sample mean of differences is approximately normal. The population mean for the differences, \(\mu_d\), is then tested using a Student's-t test for a single population mean with \(n – 1\) degrees of freedom, where \(n\) is the number of differences, that is, the number of pairs not the number of observations.
- https://stats.libretexts.org/Courses/Fresno_City_College/Introduction_to_Business_Statistics_-_OER_-_Spring_2023/10%3A_Hypothesis_Testing_with_Two_Samples/10.07%3A_Matched_or_Paired_SamplesThe population mean for the differences, \(\mu_d\), is then tested using a Student's-t test for a single population mean with \(n – 1\) degrees of freedom, where \(n\) is the number of differences, th...The population mean for the differences, \(\mu_d\), is then tested using a Student's-t test for a single population mean with \(n – 1\) degrees of freedom, where \(n\) is the number of differences, that is, the number of pairs not the number of observations. \[\textbf{The null and alternative hypotheses for this test are:}\nonumber\] \[H_{a} : \mu_{d} \neq 0\nonumber\] \[\textbf{The test statistic is:}\nonumber\] \[t_{c}=\frac{\overline{x}_{d}-\mu_{d}}{\left(\frac{s_{d}}{\sqrt{n}}\right)}\nonum…
- https://stats.libretexts.org/Courses/Saint_Mary's_College_Notre_Dame/BFE_1201_Statistical_Methods_for_Finance_(Kuter)/07%3A_Hypothesis_Testing/7.12%3A_Matched_or_Paired_SamplesWe expect that the standard deviation of the differences of the matched pairs will be smaller than unmatched pairs because presumably fewer differences should exist because of the correlation between ...We expect that the standard deviation of the differences of the matched pairs will be smaller than unmatched pairs because presumably fewer differences should exist because of the correlation between the two groups. The population mean for the differences, \(\mu_d\), is then tested using a Student's-t test for a single population mean with \(n – 1\) degrees of freedom, where \(n\) is the number of differences, that is, the number of pairs not the number of observations.
