How it departed

From the claim it replicates, Over every sample size n from 5 to 100 and every true proportion p from 0.001 to 0.999 in steps of 0.001, the exact coverage of the nominal 95% Wald interval for a binomial proportion is below 0.93 at a fraction 0.463088 of the 95904 (n, p) pairs and below 0.95 at a fraction 0.923027 of them.

• Done differently

  Scope is limited to the original Wald undercoverage claim. The original floating probability recurrence and square-root interval endpoints are replaced by direct integer binomial expansion and an integer squared-membership test. The printed decimal critical value is treated as an exact rational rather than its binary64 approximation. The grid and strict coverage thresholds are unchanged.

  Bears on C1