IntroductionStudies often compare two groups. For example, researchers are interested in the effect aspirin has in preventing heart attacks. Over the last few years, newspapers and magazines have reported about various aspirin studies involving two groups. Typically, one group is given aspirin and the other group is given a placebo. Then, the heart attack rate is studied over several years.There are other situations that deal with the comparison of two groups. For example, studies compare various diet and exercise programs. Politicians compare the proportion of individuals from different income brackets who might vote for them. Students who are interested in whether SAT or GRE preparatory courses really help raise their scores.In the previous chapter, you learned to conduct hypothesis tests on single means and single proportions. You will expand upon that in this chapter. You will compare two averages or two proportions to each other. The procedure is still the same, just expanded.To compare two averages or two proportions, you work with two groups. The groups are classified as independent and matched pairs. Independent groups mean that the two samples taken are independent, that is, sample values selected from one population are not related in any way to sample values selected from the other population. Matched pairs refer to matched or paired samples. The parameter tested using matched pairs is the population mean. The parameters tested using independent groups are either population means or population proportions.This chapter relies on either a calculator or a computer to calculate the degrees of freedom, the test statistics, and p-values. TI-83+ and TI-84 instructions are included as well as the the test statistic formulas. Because of technology, we do not need to separate two population means, independent groups, population variances unknown into large and small sample sizes. The small sample case depends on the assumption that the unknown population variances are equal. It is not necessary to make that assumption.This chapter deals with the following hypothesis tests:Independent groups (samples are independent)Two population means. Two population proportions. Matched or paired samplesSample sizes are often small. Two measurements are drawn from the same pair of individuals or objects. Two samples are combined to form one sample of differences.