29.10 Summary

Consider testing a hypothesis about a population mean difference μd, based on the value of the sample mean difference d¯. Under certain statistical validity conditions, the sample mean difference varies with an approximate normal distribution centered around the hypothesised value of μd, with a standard deviation of

s.e.(d¯)=sdn. This distribution describes what values of the sample mean difference could be expected if the value of μd in the null hypothesis was true. The test statistic is

t=d¯μds.e.(d¯), where μd is the hypothesised value in the null hypothesis. The t-score describes what value of d¯ was observed in the sample, relative to what was expected. The t-value is like a z-score, so an approximate P-value can be estimated using the 68–95–99.7 rule, or is found using software. The P-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: