Joe Sutton is evaluating the effects of the 1987 market decline on the volume of trading. Specifically, he wants to test whether the decline affected trading volume. He selected a sample of 500 companies and collected data on the total annual volume for one year prior to the decline and for one year following the decline. What is the set of hypotheses that Sutton is testing? A) H0: µd ≠ µd0 versus Ha: µd = µd0. B) H0: µd = µd0 versus Ha: µd ≠ µd0. C) H0: µd = µd0 versus Ha: µd > µd0. The answer is B Explaination by Schweser Qbank-- This is a paired comparison because the sample cases are not independent (i.e., there is a before and an after for each stock). Note that the test is two-tailed, t-test. Can anyone explain?
We test whether the 1987 stock crash affected volume trading. The question does not specify the direction (increase or decrease) so we use 2 tails test. And yet, since the population is the same, 500 companies, so we use match pair or pair comparison. Match pair also uses t test. The thing that you should focus on judging the independent of 2 populations, if they are related, we should use match pair. A typical example of match pair is a tires manufacture want to test its product versus competitors. The manufacturer product is put in the right rear and competitor in the left. The car runs straightly that is equally effect on both sides. Even 2 populations are different but they are under the same influence, they are related. However, in my statistic final exam last year, students usually seek for the key words such as before, after to recognize match pair but most of my friend were wrong. The question was a marketing manager want to test the effectiveness of a new ad. Sales of 4 weeks before and after the ad are randomly collected among various stores and tested. The test here is independent not match pair. So even the questions might sound familiar, they are not. In this case, if the question was sales in particular stores or days in week, the test is match pair.