Confidence Intervals

The one idea: A confidence interval takes a point estimate and wraps it in a range wide enough to admit what the point estimate can't: sampling wobble. Build it by reaching out from your estimate by a multiplier (from the normal curve if σ is known, from the t distribution if it isn't) times the standard error — and the "95%" attached to it is a statement about the procedure, not a probability about the specific range you just computed.

⚠️ The trap: "There's a 95% probability the true conversion rate is between 40.8% and 47.2%." That feels right and it's almost universally how people say it, and it's wrong. The true rate is a fixed number — it's not rolling dice — so it either sits inside your interval or it doesn't; the 95% describes how often the method you used lands on the truth across repeated samples, and this is a single run of that method. This single misreading is the most common statistical error in circulation, repeated in board meetings, press coverage, and dashboards by people who computed the interval correctly and then explained it wrong.

A point estimate is a promise with no fine print: "conversion rate is 44%," full stop, no mention of how much that number would move if you resampled tomorrow. A confidence interval is the fine print made explicit — a range that says "the true value is very likely somewhere in here" and, crucially, quantifies exactly what "very likely" means. It's built from exactly two ingredients you already have: the point estimate, and the standard error that describes how much that estimate wobbles from sample to…