27.7 Communicating results: One mean

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 \(37.0^\circ\text{C}\) (\(\bar{x} = 36.81\); \(n=130\); 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): ‘\(\bar{x} = 36.81\); \(n=130\); 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.