Once we have the one data set (which, again, represents the *difference* between the two populations), we need to calculate both the mean and standard deviation of this new data set and then use the same hypothesis test steps and formulas as before. The only change is the act of subtracting the matched-pairs data to obtain one sample. And remember, since we do not know the exact value of the population standard deviation of the difference, *σ _{d}*, we must estimate

*σ*with the sample standard deviation of the difference,

_{d}*s*. Therefore, we cannot use the standard normal distribution and must instead rely on the Student’s

_{d}*t*-distribution. As usual, focus on the

*P*-value approach to calculating confidence intervals and performing hypothesis tests.