Mistake Master
Every Rule in the Setup Is a Promise About How Often You Are Wrong
You'll learnwhy both hypotheses are claims about the parameter and never about the sample, where the alternative's direction comes from, why the conditions and the standard error use the hypothesized proportion, what the significance level is committing to — and what each of those rules costs in false alarms when it is broken after the data arrive.
A company claims 40% of its customers renew. A manager suspects it is lower, surveys 250 randomly chosen customers, and finds 88 renewals — a sample proportion of 0.352. Setting up the test means writing four things down before any of that arithmetic happens: the parameter in context, the two hypotheses, the conditions with their numbers, and the significance level. Those rules sound like etiquette, and this page prices them instead. Under a null that is exactly true, a one-sided test at the 5% level rejects 5.24% of the time — as advertised. Choose which tail to use after seeing which way the sample fell, and the same test rejects 10.64% of the time: a promise of one false alarm in twenty, delivering one in nine. And this sample's p-value is 0.0607, sitting between the two most common significance levels, so a level chosen after the fact decides the verdict by itself.