Bootstrap Confidence Intervals (CIs)
Sort 500 resampled values and read off two percentiles. That is the whole method, and it works for statistics that have no convenient formula.
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Margin of Error (MoE)
A margin of error needs a confidence level to exist. Quote one without it and you are off by the multiplier — about a factor of two at 95%.
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Proportion
Enumerated exactly, not simulated: the Wald interval delivers 0.8775 where it promises 0.95.
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True Population Parameter
Split the same outcomes by what was observed and coverage runs from 1.0000 to 0.5979.
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Post Hoc Power Analysis
Observed power and the p-value are two readings of the same statistic. A near-miss result will always come back as low power.
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Confidence Level
95% is a property of the method, not of the interval in front of you. A higher level targets greater coverage across samples and usually widens the interval; it does not assign a posterior probability to the observed interval.
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Wilson Score Interval
The textbook proportion interval can put its lower bound below zero. Inverting the test instead gives bounds that stay inside the range.
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Bootstrap
The bootstrap gives you a sampling distribution for statistics that have no convenient formula. What it cannot give you is a fix for a biased sample.
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Confidence Intervals (CIs)
95% describes the procedure across repeated samples, not your confidence in this particular interval. The distinction changes how you report it.
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Noninferiority Margin
A noninferiority test asks whether a new option is worse than the old one by no more than a margin chosen in advance, and it passes only when the confidence interval’s lower bound clears that margin.