Use sample data to estimate population means/proportions and develop margins of error using simulation.
State confidence as repeated-method capture
Problem
The displayed \(95\%\) confidence interval is \([0.41,~0.49]\) for a fixed population proportion \(p\). Interpret \(95\%\) confidence using repeated random sampling and interval construction.
Confidence belongs to the sampling-and-interval procedure, not to a changing population parameter. Across repeated random samples, the parameter stays fixed while the computed interval varies; the confidence level is the long-run fraction of those intervals that capture the parameter under the method's conditions. Once one interval is computed, it either contains the parameter or it does not.
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