Problem

Estimate \(A\) is \(52\%\) \(\pm~\) \(4~\text{percentage}~\text{points}\), and estimate \(B\) is \(55\%\) \(\pm~\) \(4~\text{percentage}~\text{points}\). Compute \(\text{both}~\text{intervals}\), find their overlap, and interpret what the overlap does and does not establish.

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Ignore both margins, compare 52% with 55%, and declare B definitively larger.

A: 52%±4 points is 48%–56%. B: 55%±4 points is 51%–59%. They overlap from 51% to 56%, so the observed difference is not clearly distinguishable; overlap does not prove equality.

Use the correct intervals 48%–56% and 51%–59%, but say their overlap proves the population proportions are equal.

Use 4% of each estimate: A≈49.92%–54.08% and B≈52.80%–57.20%.

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Estimate \(A\) is \(52\%\) \(\pm~\) \(4~\text{percentage}~\text{points}\), and estimate \(B\) is \(55\%\) \(\pm~\) \(4~\text{percentage}~\text{points}\). Compute \(\text{both}~\text{intervals}\), find their overlap, and interpret what the overlap does and does not establish.

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