We would like to know if Intel’s stock and Southwest Airlines’ stock have similar rates of return. To find out, we take a random sample of 50 days, and record Intel’s and Southwest’s stock on those same days.

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BlackTom AI · Accepted Answer

To analyze the question, first restate the setup: researchers are sampling 50 days and recording Intel’s stock and Southwest Airlines’ stock on those same days. This design pairs observations of two stocks taken at the same time points.
Option 1: 'Paired' — This choice aligns with the data collection method described. Because each day provides two related measurements (Intel and Southwest on the same day), the observations are naturally paired, and the comparison between the two stocks should account for this pairing.
Option 2: 'Not Paird' — This option suggests that the two sets of observations are independent or unpaired, which would be inappropriate here since the data for Intel and Southwest are collected on the same days, creating a natural linkage between the two measurements for each day. Treating them as unpaired would ignore the within-day connection and could distort analyses that rely on the paired structure.
Additional nuance: when the goal is to compare rates of return between two assets over the same time horizon, pairing by day allows for methods that exploit the day-to-day relationship, such as calculating difference in returns per day or conducting a paired t-test, which increases statistical efficiency by controlling for day-specific market effects. Conversely, treating the data as unpaired would fail to leverage this information and could lead to less precise inferences.
In summary, the described sampling design inherently creates paired observations because both stocks are measured on the same days, making the 'Paired' option the appropriate characterization, while the 'Not Paird' option mischaracterizes the data structure by implying independence between the two series.

FA25_QTM_100_3 7.18: Paired or not? Part II.

We would like to know if Intel’s stock and Southwest Airlines’ stock have similar rates of return. To find out, we take a random sample of 50 days, and record Intel’s and Southwest’s stock on those same days.

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