Consider two sets of data that are paired with each other. Each observation in one data set has a natural correspondence with exactly one observation from the other data set.

Question

BlackTom AI · Accepted Answer

Consider the concept of paired data: when two data sets are paired, each observation in one set corresponds to exactly one observation in the other set. This one-to-one correspondence is what defines a paired design.
Option 1: True. This statement aligns with the standard definition of paired data, where there is a natural, exact match between observations across the two sets, ensuring each pair shares a common index or subject.
Option 2: False. The claim would be false if there were either many-to-one or one-to-many mappings, or if no natural pairing existed between observations. In those situations, the data would not be properly considered paired as described, which contradicts the premise given.
Option 3: True, but with caveats. While the core idea is correct, one might worry about missing pairs or duplicate matches in some real-world datasets. However, as stated, the definition presumes a proper one-to-one pairing, so the statement remains accurate under that assumption.
Option 4: False, if the pairing were arbitrary rather than natural. If there was no natural correspondence and the pairing was random, the data would be paired but not in a meaningful associated way; yet the question emphasizes a natural correspondence, which preserves the True assessment.
In summary, the essential feature of paired data in this context is the one-to-one, natural correspondence between observations, which makes the statement True.

FA25_QTM_100_3 7.16: True / False: paired.

Consider two sets of data that are paired with each other. Each observation in one data set has a natural correspondence with exactly one observation from the other data set.

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