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 $37.0^\circ\text{C}$ :