TESTING TWO POPULATION MEANS AND PROPORTIONS 71 Test Statistic: Observed Significance Level: To find the p- value for the t test statistic, we use the function in Excel =tdist(1.9798,24,1). p- value = 0.02965 Conclusion: Since the test statistic of t = 1.9798 falls above the critical bound of t = 1.1711, we reject H 0 with at least 95% con- fidence. Likewise, since the p- value of 0.02965 is less than the desired of 0.05, we reject H 0 . There is enough evidence to con- clude that the new advertising campaign is effective in increasing the daily sales revenues for franchises in the chain. The z- Test for Differences Between Two Proportions As municipal, state, and national election polls predict popular support for favored candidates and causes, the estimation and comparison of pop- ulation proportions play an important role in anticipating and expressing the voice of the people and their democratic decisions. Preelection polls boast support for this or that candidate or cause at a certain level, within plus or minus a stated percent. There are few statistical topics as widely publicized or as important to the conduct of political processes as the estimation and comparison of population proportions. The difference between two population proportions plays an equally important role in business, in market research, business forecasting, financial auditing, and analysis of comparative defect rates, to name a few. At the heart of the proportion is a count, not a measurement, of sampled elements. When we sort a sample into subgroups--those elements that do meet a certain criterion and those that do not--and then produce a count of these sub- groups, we use a proportion to compare the results. Inferences about (p 1 ­ p 2 ) are based on two random samples from two unrelated populations. The two samples do not have to be the same size. We summarize the sample statistics for each, including sample sizes, the number of successes in each sample, and the sample proportions. The