Problem

Using the stated descriptive rule, compare group A's yes rate of \(140/200=70\%\) with group B's rate of \(60/200=30\%\). Under thresholds of at most \(5~\text{points}\) for approximate independence and at least \(10~\text{points}\) for association, which conclusion is supported?

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What this problem is really about

To study association, compare the same outcome rate within each group rather than comparing raw counts. Subtract the conditional percentages in percentage points, apply the stated descriptive threshold, and use the order of the rates to report direction while keeping the conclusion noncausal.

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difference=|70%-30%|=40 percentage points≥10; classification=descriptive association; direction=Group A has a 40-point higher yes rate

difference=|70%−30%|=40 percentage points≥10; classification=approximate independence; direction=30% is treated as A's no rate so groups match

difference=|70%−30%|=40 percentage points≥10; classification=no association because both have yes responses; direction=Group A is 40 points higher

difference=70%+30%=100 percentage points; classification=independent because percentages sum100; direction=the groups are treated as matching

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Using the stated descriptive rule, compare group A's yes rate of \(140/200=70\%\) with group B's rate of \(60/200=30\%\). Under thresholds of at most \(5~\text{points}\) for approximate independence and at least \(10~\text{points}\) for association, which conclusion is supported?

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