Using R for Introductory Statistics : John Verzani

Confidence intervals 195contains the place of the runner in the sample and is randomly sampled from all thepossible places.7.5 Confidence intervals for differencesWhen we have two samples, we might ask whether the two came from the samepopulation. For example, Figure 7.5 shows results for several polls on presidentialapproval rating from early 2001 to early 2004. * The rating varies over time, but for anygiven time period the polls are all pretty much in agreement. This is to be expected, as thepolls are tracking the same population proportion for a given time period. However, howcan we tell if the differences between polls for different time periods are due to a changein the underlying population proportion or merely an artifact of sampling variation?7.5.1 Difference of proportionsWe compare two proportions when assessing the results of surveys, as with the approvalratings, but we could do the same to compare other proportions, such as market shares.To see if a difference in the proportions is explainable by sampling error, we look atand find a confidence interval for p 1 −p 2 . This can be done, as* A similar figure appeared in a February 9, 2004, edition of Salon (http://www.salon.com/). Thedata is in the data set BushApproval (UsingR), and the graphic can be produced by runningexample(BushApproval).the statisticFigure 7.5 Presidential approvalrating in United States from spring2001 to spring 2004