Problem

The displayed estimates are \(A~=~52\%~\pm~3~\text{points}\) and \(B~=~44\%~\pm~3~\text{points}\). Compute \(\text{both}~\text{intervals}\), find their gap or overlap, and apply the stated informal rule without claiming a formal significance test.

Neutral interval-comparison scaffold for A = 52% ± 3 points and B = 44% ± 3 points; it withholds endpoint, overlap, and conclusion information.

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What this problem is really about

Compute both uncertainty intervals before comparing their nearest endpoints. If one interval ends below where the other begins, subtract those endpoints to measure the gap; otherwise describe their overlap. Apply only the informal rule explicitly requested, because overlap or nonoverlap of separate intervals is not by itself a formal hypothesis test or a p-value.

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A is [49%, 55%] and B is [41%, 47%]. They have a 2-point gap, which establishes a formal p-value and statistically significant difference.

A is [49%, 55%] and B is [41%, 47%]. They have a 2-point gap, so the informal nonoverlap rule suggests a difference; this is not a formal significance test.

A is [49%, 55%] and B is [41%, 47%]. They have a 2-point gap, so the informal rule gives no clear difference; this is not a formal significance test.

Ignore the margins and use A = [52%, 52%] and B = [44%, 44%]. Their 8-point gap suggests a difference under the informal rule, but this is not a formal significance test.

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The displayed estimates are \(A~=~52\%~\pm~3~\text{points}\) and \(B~=~44\%~\pm~3~\text{points}\). Compute \(\text{both}~\text{intervals}\), find their gap or overlap, and apply the stated informal rule without claiming a formal significance test.

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