Problem

A probability sample estimates \(58\%~\pm~4~\text{percentage}~\text{points}\). Compute the interval and assess the claim \(p~>~50\%\), retaining the population scope and sampling uncertainty.

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What this problem is really about

Audit the sampling design before using an interval for a population claim. Compute both endpoints, then compare the entire interval with the directional threshold; the conservative endpoint determines whether every plausible value lies on the claimed side. Keep the conclusion limited to the frame population and retain sampling, nonresponse, and coverage uncertainty rather than treating interval support as proof.

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Treat the sample as nonrandom but still use [54%, 62%], entirely above 50%, to support a majority claim for the full population without limits.

Use only the estimate 58% > 50% and ignore the interval. Any point estimate above 50% proves a majority claim for the population.

The interval is [54%, 62%], entirely above 50%, so it cautiously supports a majority claim for the frame population, with sampling uncertainty.

The probability-sample interval is [54%, 62%], entirely above 50%, so it proves the majority claim for the frame population with no sampling uncertainty.

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A probability sample estimates \(58\%~\pm~4~\text{percentage}~\text{points}\). Compute the interval and assess the claim \(p~>~50\%\), retaining the population scope and sampling uncertainty.

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