Section 10.2 Summary

1. Section 10.2 examines inferential methods for ${\mu }_1-{\mu }_2$, which is the difference between the means of two independent populations. Two-sample $t$ tests may be performed using either the $p$-value method or the critical-value method.
2. $100(1-\alpha )\%$ $t$ confidence intervals for ${\mu }_1-{\mu }_2$ are developed and illustrated.
3. The use of $t$ confidence intervals for ${\mu }_1-{\mu }_2$ to perform two-tailed $t$ tests is illustrated.
4. The pooled variance method for $t$ inference may be applied when the data analyst has reason to believe that the variances of the two populations are equal.
5. When the population standard deviations ${\sigma }_1$ and ${\sigma }_2$ are known, the data analyst may prefer to use $Z$ inference for ${\mu }_1-{\mu }_2$.