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