3.2 Difference of two means

In this section we consider a difference in two population means, ${\mu }_1-{\mu }_2$, under the condition that the data are not paired. The methods are similar in theory but different in the details. Just as with a single sample, we identify conditions to ensure a point estimate of the difference ${\overline{x}}_1-{\overline{x}}_2$ is nearly normal. Next we introduce a formula for the standard error, which allows us to apply our general tools from Section 2.11.

We apply these methods to two examples: participants in the 2013 London Marathon and newborn infants. This section is motivated by questions like ‘‘Is there convincing evidence that newborns from mothers who smoke have a different average birth weight than newborns from mothers who don’t smoke?’’