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

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This statement is true. According to the principles of matched pairs experiments, we are comparing the means of two populations with dependent samples. Therefore, we use the t-test for paired samples. The test statistic for the t-test is Student t-distributed with v = n-1 degrees of freedom, where n is the number of pairs. In this case, the formula for the test statistic includes the difference between the means, which is divided by the standard error of the differences. If the differences are normally distributed, then the t-test is appropriate and the test statistic follows a Student t-distribution with the specified degrees of freedom.

When Comparing Two Population Means Using Data That Are Gathered μ\muμ

When Comparing Two Population Means Using Data That Are Gathered $\mu$