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