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Paired t

The Paired t conducts a hypothesis test of the difference between two population means when observations are paired. It also calculates a confidence interval of the difference. This procedure is based on the t-distribution which is derived from a normal distribution. It is appropriate when the paired differences follow a normal distribution. If the observations are dependent in a pairwise manner, the matching results in smaller variance and greater power of detecting differences than the 2-sample t.

Test Null Hypothesis, H0 Alternate Hypothesis, H1
One-tailed μd = μD μd < μD or μd > μD
Two-tailed μd = μD μd ≠ μD

where μd is the population mean of the differences and μD is the hypothesized mean of the differences