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Chapter 7. Hypothesis Testing > 7.3 P Values - Pg. 192

192 Chapter 7 who put in the big blind must either bet or fold before they see the three-card flop. Thus, looseness generally measures how often a person puts money into the pot in order to see the flop cards. Tight players fold when the two cards they hold are not strong; loose players stay in, hoping that a lucky flop will strengthen their hand. At six-player tables, people are considered to be very tight players if their looseness is below 20 percent and to be extremely loose players if their looseness is above 50 percent. We look at two research questions: 1. Do these players tend to have a loose or tight style of play? 2. Is their style of play different after a big loss than after a big win? To answer the first research question, we make an assumption, called the null hypothesis (or H 0 ), about the population from which the sample is drawn. Typically, the null hypothesis is a "straw assumption" that we anticipate rejecting. To demonstrate, for example, that a medicine is beneficial, we see whether the sample data reject the hypothesis that there is no (null) effect. Here, the null hypothesis might be that the average looseness coefficient is 35, which is halfway between 20 (tight) and 50 (loose). Although we expect experienced high-stakes players to have a relatively tight style of play, the way to demonstrate this by statistical contradiction is to see if the evidence rejects the straw hypothesis that the average looseness coefficient is 35. The alternative hypothesis (usually written as H 1 ) describes the population if the null hypothesis is not true. Here, the natural alternative hypothesis is that the population mean is not equal to 35: H 0 : = 35 H 1 : 35 The alternative hypothesis is usually two sided, because even though we might have a hunch about how the study will turn out, we are reluctant to rule out beforehand the possibility that the population mean may be either lower or higher than the value specified by the null hypothesis. If, before seeing the data, we could rule out one of these possibilities, the alternative hypothesis would be one sided. If, for example, we were convinced beforehand that the average looseness coefficient of experienced players could not possibly be higher than 35, the one-sided alternative hypothesis would be H 1 : < 35. 7.3 P Values Once we have specified the null and alternative hypotheses, we analyze our sample data. Because we want to test a null hypothesis about the population mean, we naturally look at the sample mean--because the sample mean is what we use to estimate the value of the population mean. The estimator used to test the null hypothesis is called the test statistic. www.elsevierdirect.com