Step 1: Anchor the definition on the word "paired": the two sets of values must come from the same subjects, not from independent groups.
Step 2: The typical use is measuring a quantitative variable on each person, applying an intervention, then measuring again, and testing whether the within-person change (the before-after difference) is significant.
Step 3: Qualitative proportions need chi-square (rules out one option) and two unrelated groups need the unpaired t-test (rules out another), leaving the before-and-after quantitative comparison as the defining feature of the paired t-test. \[\boxed{\text{Quantitative observations before and after an intervention}}\]