27.8 Hypothesis testing: A summary

Let’s recap the decision-making process seen earlier, in this context about body temperatures:

Step 1: Assumption: Write the null hypothesis about the parameter (based on the RQ): \(H_0\): \(\mu=37.0^\circ\text{C}\). In addition, write the alternative hypothesis \(H_1\): \(\mu\ne 37.0^\circ\text{C}\). (This alternative hypothesis is two-tailed.)
Step 2: Expectation: The sampling distribution describes what to expect from the sample statistic if the null hypothesis is true: under certain circumstances, the sample means will vary with an approximate normal distribution around a mean of \(\mu=37.0^\circ\text{C}\) with a standard deviation of \(\text{s.e.}(\bar{x}) = 0.03572\) (Fig. 27.3).
Step 3: Observation: Compute the \(t\)-score: \(t=-5.45\). The \(t\)-score can be computed by software, or using the general equation (27.1).
Step 4: Consistency?: Determine if the data are consistent with the assumption, by computing the \(P\)-value. Here, the \(P\)-value is much smaller than 0.001. The \(P\)-value can be computed by software, or approximated using the 68–95–99.7 rule.

The conclusion is that there is very strong evidence that \(\mu\) is not \(37.0^\circ\text{C}\):