Mistake Master
The Interval Is a Claim About One Number It Never Sees
You'll learnhow a one-proportion z-interval is assembled from an estimate and a margin of error, which proportion goes into the standard error and why, what the three conditions look like when they are actually checked, what the confidence level is a property of — demonstrated by computing the method's exact capture rate — and the one interpretation sentence that survives grading.
Of 400 randomly selected voters, 248 support a measure. The point estimate is 0.62, and the 95% confidence interval is 0.62 ± 1.96 × 0.0243 — the interval (0.572, 0.668), a range of plausible values for the one number the survey never sees. This page then does what is usually left to hand-waving: it computes what "95%" actually describes. Supposing a truth of 0.60, all 401 possible samples of 400 are built into intervals and their capture probabilities summed exactly — the method delivers 94.7%, and the page draws nine ranked samples, seven catching the truth and the two extreme ones missing it. What 95% does not describe gets its numbers too: the share of voters whose 0-or-1 values land inside the interval is exactly zero, and the chance a future sample proportion lands in this interval works out to 87.7%. One sentence survives, and it names the parameter. Twelve short steps; press Next for each one.