Hypothesis Testing

1. Decide on a claim and an alternative claim. (Null hypothesis must have an “equal” in it. Alternative hypothesis usually has the claim that will cause you to “spend money” or “change something” if you decide that it is true.) 2. Choose a test statistic to summarize the data, whose sampling distribution if the null hypothesis is true can be determined, and which depends on the parameter of interest. 3. Determine which values of the test statistic would support the alternative hypothesis. 4. Compute the p-value of the data: the probability of getting data at least as far from the null hypothesis as the data we got, in the direction of the alternative hypothesis, if the null hypothesis is true. (Often, a sketch of the sampling distribution of the test statistic, assuming the null hypothesis is true, with the data, and the area for the p-value shaded in, is useful.) 5. If the p-value is small, then the data provide strong evidence against the null hypothesis. If the p-value is not small, then the data do not provide strong evidence against the null hypothesis.