Hypothesis tests: Poisson, binomial and normal means

Last time

Before we start: last time, in The Central Limit Theorem and confidence intervals, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

Is the change real?

A factory installs new safety rules and has fewer accidents the next week. Was it the rules, or just luck? A hypothesis test answers that. It asks: if nothing had changed, how unlikely would this result be? If it is very unlikely, say less than five percent, you reject the idea that nothing changed.

The steps of a test

State the null hypothesis, H zero, that nothing has changed, and the alternative, H one, that it has. Assume H zero is true. Work out the probability of a result as extreme as the one observed. Compare with the significance level. If smaller, reject H zero. Then state a conclusion in context.

Writing hypotheses

Use the parameter: the population mean, or p, the population proportion. Not just the word mean. H one has a direction when the question suggests one. Has increased gives greater than. Has reduced gives less than. Is different gives not equal. A one-tail test puts all of the significance level in one tail. A two-tail test splits it between both.