Binomial Test

Binomial Test — is your proportion really different from the claim?

You flipped a coin 50 times and got 36 heads. Is the coin fair, or is 36 too many to be luck? Binomial Test answers exactly this kind of yes/no question: you have k successes out of n trials, and you want to know whether the true success rate really differs from a claimed value p0. No data lists, no guesswork — just the counts, computed exactly.

Everything runs offline on your device. Nothing is uploaded.

WHAT IT DOES
• Exact binomial test — the p-value is computed exactly (not a normal approximation), so it stays accurate even for small samples.
• One-sided and two-sided — ask "is p different from p0?", "is it greater?", or "is it less?".
• Wilson 95% confidence interval — a reliable range for the true proportion; if it excludes p0, the result is significant.
• Observed vs expected — see your proportion p-hat next to the claimed rate at a glance.

EASY, FLEXIBLE INPUT
• Type the exact numbers, or drag the slider — your choice.
• Handy minus / plus stepper buttons for quick one-at-a-time adjustments.
• Pick successes k, trials n and the claimed probability p0 in seconds.

CLEAR VISUALS
• Binomial PMF bar chart with your observed count highlighted and the rejection region shaded — you can literally see the p-value add up.
• Proportion-and-confidence-interval line showing p-hat, the interval, and the claim p0 together.
• Beautiful, distraction-free "cranberry" design.

LEARN THE CONCEPT
• Plain-language explanations of the binomial setup, the exact p-value, and confidence intervals.
• Crisp mathematical formulas rendered with KaTeX — fully offline, never overlapping or cut off.

COIN-FLIP SIMULATOR
• Rig a coin's true bias, flip it n times, and test it for fairness.
• See for yourself why a slight bias is hard to catch with few flips but easy with many.

WORKED EXAMPLES
• Is the coin fair? (36 of 50)
• A free-throw claim of 80% — but only 33 of 50 made.
• A factory defect target of 5% vs 16 defects in 200.

WHO IT IS FOR
• Students learning statistics and hypothesis testing.
• Teachers who want a clean, visual demonstration.
• Anyone who needs a quick, exact binomial test on the go.

Small, fast, offline, and ad-supported. Download Binomial Test and find out whether your result is real or just chance.