29.10 Summary
Consider testing a hypothesis about a population mean difference , based on the value of the sample mean difference . Under certain statistical validity conditions, the sample mean difference varies with an approximate normal distribution centered around the hypothesised value of , with a standard deviation of
This distribution describes what values of the sample mean difference could be expected if the value of in the null hypothesis was true. The test statistic is
where is the hypothesised value in the null hypothesis. The -score describes what value of was observed in the sample, relative to what was expected. The -value is like a -score, so an approximate -value can be estimated using the 68–95–99.7 rule, or is found using software. The -values helps determine if the sample evidence is consistent with the assumption, or contradicts the assumption.
The following short video may help explain some of these concepts: