When comparing two population means using data that are gathered from a matched pairs experiment, the test statistic for m _D is Student t -distributed with v = n_D - 1 degrees of freedom, provided that the differences are normally distributed.

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In a matched pairs experiment, the test statistic for comparing two population means is indeed Student t-distributed with $v = n - 1$ degrees of freedom, assuming the differences between the paired observations are normally distributed. This is because the analysis essentially involves one sample of paired differences.

When Comparing Two Population Means Using Data That Are Gathered