Methods · interval estimates for proportions · manipulative

Do confidence intervals cover p?

Each sample builds its own width from p̂(1−p̂). Most intervals cover the true p — but not all, and skinny extreme samples miss more often.

covers p misses p true p

Dashed line is p · bar length = that sample’s MoE · grow the bank or change p / n / level

20

How many CIs on the plot. Widths differ because each sample has its own p̂.

0.50
40
95%

Changing p redraws samples. n recomputes each p̂ from stored Bernoulli draws; level only resizes widths.

Coverage

intervals
0
contain p
0
hit rate
target
95%