Suppose some scientists are testing the hypothesis that a drug has probability .8 of curing a patient, with each patient independent of the others. The scientists try the drug on many patients, and it only cures half of them: k = n/2. In fact, the number of cured patients isn't even 3 standard deviations below the mean: k .99 If the hypothesis they are testing is true, the probability of k successes was .01 If the hypothesis they are testing is true, the probability of k successes was s .05