10.4 Tests of hypotheses
Hypothesis testing is covered in detail in most mathematical statistics texts. This review is fairly straightforward and does not address philosophical issues or consider alternative approaches. A hypothesis test begins with two hypotheses, one called the null and one called the alternative. The traditional notation is H0 for the null hypothesis and H1 for the alternative hypothesis. The two hypotheses are not treated symmetrically. Reversing them may alter the results. To illustrate this process, a simple example is used.
Your company has been basing its premiums on an assumption that the average claim is 1,200. You want to raise the premium, and a regulator has insisted that you provide evidence that the average now exceeds 1,200. To provide such evidence, the following numbers have been obtained:
What are the hypotheses for this problem?
Let μ be the population mean. One hypothesis (the one you claim is true) is that μ > 1,200. Because hypothesis tests must present an either/or situation, the other hypothesis must be μ ≤ 1,200. The only remaining task is to decide which of them is the null hypothesis. Whenever the universe of continuous possibilities is divided in two, there is likely to be a boundary that needs to be assigned to one hypothesis ...