We randomly sample 50 items from Target stores and note the price for each. Then we visit Walmart and collect the price for each of those same 50 items.

Question

BlackTom AI · Accepted Answer

We start by restating the scenario to ensure clarity about the study design and data structure.
The situation involves taking price measurements for 50 items at Target, and then obtaining the prices for the same 50 items at Walmart, creating a set of 50 paired observations (one Target price and one Walmart price for each item).
Option 1: 'Not Paired' would imply that the price observations are independent or that there’s no natural one-to-one correspondence between Target and Walmart prices for the same item. This would be incorrect because each item has two related price measurements tied to the same product, forming pairs.
Option 2: 'Paired' correctly reflects the design where each item yields a pair of related measurements (Target price and Walmart price). This pairing leverages the link between the two measurements for the same item, which is essential for analyses that account for within-item comparison or changes from one store to another.
To evaluate why 'Paired' is the appropriate classification, consider how the data are collected: for every item i in 1 to 50, we record Target price T_i and Walmart price W_i. The pair (T_i, W_i) is linked by the item identity, making the observations across stores non-independent within the same item. Treating them as independent would ignore this inherent connection and could lead to biased inferences about price differences.
Furthermore, a paired design is advantageous when the goal is to assess price differences or changes between the two stores while controlling for item-specific price levels, since each item serves as its own control. This design naturally supports analyses such as computing the difference D_i = W_i − T_i and performing a paired t-test or nonparametric equivalent on the D_i values.
In contrast, if one were to misclassify the design as 'Not Paired,' the interpretation would fail to exploit the item-wise linkage, and any method assuming independence between Target and Walmart prices across items would be inappropriate for this context.
Collectively, the correct conceptual takeaway is that the study uses paired observations, because each item provides two related measurements across two conditions (Target and Walmart) that are matched by item identity.

FA25_QTM_100_3 7.18: Paired or not? Part II.

We randomly sample 50 items from Target stores and note the price for each. Then we visit Walmart and collect the price for each of those same 50 items.

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