The Germination Test That Tells the Truth: How Many Seeds a Farmer Must Test Before a Result Can Be Trusted

Before sowing saved seed, many farmers test a handful — ten, twenty, or twenty-five seeds on a wet cloth — and trust the percentage that sprouts. This paper computes, with exact binomial (Clopper–Pearson) arithmetic, what such tests can and cannot certify. A perfect result is weaker than it looks: 10 of 10 seeds germinating certifies only that the lot's true germination is at least 69.2% at 95% confidence; 20 of 20 certifies 83.2%; 25 of 25 certifies 86.3%; and at least 23 consecutive germinations are needed before a perfect test certifies the 85% sowing-quality threshold at all. A realistic good result is weaker still: 9 of 10 (90% observed) carries an exact 95% interval of 55.5% to 99.7%, and 18 of 20 carries 68.3% to 98.8%. To estimate germination within ±10, ±5, and ±3 percentage points at 95% confidence near the 85% threshold requires planning samples of 49, 196, and 545 seeds respectively (97, 385, and 1068 in the worst case at 50%). The decision consequence is direct: under a pass rule of at least 85% observed, a 10-seed test passes a lot whose true germination is only 75% with probability 0.244, one whose true germination is 80% with probability 0.3758, and even rejects a genuinely 90% lot with probability 0.2639. The handful test can certify that a lot is not disastrous and can justify a cautious sowing-rate correction based on the interval's lower bound (a factor of 1.80 after 9 of 10, against the naive 1.11); it cannot distinguish 85% from 75%, and no decision that turns on that distinction should rest on it. The study is simulated, not measured: all results are exact arithmetic on the binomial model stated in the text.