27.7 Communicating results of a hypothesis test

In general, to communicate the results of any hypothesis test, report:

• An answer to the RQ;
• The evidence used to reach that conclusion (such as the $t$-score and $P$-value—including if it is a one- or two-tailed $P$-value); and
• Some sample summary information, including a CI, summarising the data used to make the decision.

So write:

The sample provides very strong evidence ($t=-5.45$; two-tailed $P<0.001$) that the population mean body temperature is not ${37.0}^{\circ }\text{C}$ ($\overline{x}=36.81$; $n=130$; 95% CI from 36.73${}^{\circ }$C to 36.88${}^{\circ }$C).

The components are:

• The answer to the RQ: ‘The sample provides very strong evidence… that the population mean body temperature is not ${37.0}^{\circ }\text{C}$.’
• The evidence used to reach the conclusion: ‘$t=-5.45$; two-tailed $P<0.001$.’
• Some sample summary information (including a CI): ‘$\overline{x}=36.81$; $n=130$; 95% CI from 36.73${}^{\circ }$C to 36.88${}^{\circ }$C.’

Notice how the conclusion is worded: There is evidence to support the alternative hypothesis. In fact, the alternative hypothesis may or may not be true… but the evidence (data) available supports the alternative hypothesis.