Many experiments involve a comparison of population means. For instance, a sociologist may want to estimate the difference in mean life expectancy between inner-city and suburban residents. Or a consumer group may want to test whether two major brands of food freezers differ in the average amount of electricity they use. Or a professional golfer might be interested in comparing the mean driving distances of several competing brands of golf balls travel when struck with the same club. In this chapter, we consider techniques for using two (or more) samples to compare population means.

The same procedures that are used to estimate and test hypotheses about a single population can be modified to make inferences about two populations. As in Chapters 5 and 6, theThe methodology used will depend on the sizes of the samples and the parameter of interest (i.e., the target parameter). Some key words and the type of data associated with the parameters covered in this chapter are listed in the following box.

Alternate View

Determining the Target Parameter

Parameter	Key Words or Phrases	Type of Data	Number of Samples
${\mu }_1-{\mu }_2$	Mean difference; difference in averages	Quantitative	2 independent samples
${\mu }_d$	mean of paired differences	Quantitative	1 paired sample
${\mu }_1,{\mu }_2\dots ,{\mu }_k$	Compare multiple means (averages)	Quantitative	k independent samples

You can see that the key words difference and compare help identify the fact that two populations are to be compared. In the previous examples, the words mean in mean life expectancy and average in average amount of electricity imply that the target parameter is the difference in population means, ${\mu }_1-{\mu }_2.$ We will learn that if the sample consists of paired differences, then the parameter is ${\mu }_d.$ the mean of the population of differences. Finally, you may want to compare three or more population means, ${\mu }_1$, ${\mu }_2$, ${\mu }_3$, etc.

As with inferences about a single population mean.