CHAPTER 11: MORE ABOUT HYPOTHESIS TESTING Key Terms Twotailed or nondirectional test -~ Rejection region are located in both tails of the distribution. Onetailed or directional test ~~~ Rejection region is located in just one tail of the distribution. Type I erro Rejecting a true null hypothesis. Type II erro -- Retaining a false null hypothesis. Effect -- Any difference between a true and a hypothesized population mean. Hypothesized sampling distributio - Centered about the hypothesized population mean, this distribution is used to generate the decision rule. True sampling distribution --- Centered about the true population mean, this distribution produces the one observed mean (or 2). Alpha (a) The probability of type I error, that is, the probability of rejecting a true null hypothesis. Beta \"E1 -- the probability of type II error, that is, the probability of retaining a false null hypothesis. Power (1- E) - the probability of detecting a particular effect. Power curves --- Show how the likelihood of detecting any possible effect varies with different sample sizes. Text Review Section I The importance of hypothesis tests is that they allow the researcher to beyond existing data. In this process, the helps the researcher assess the effects of chance. If the researcher rejects a true null hypothesis, he would make a It would be a error if the researcher retains a false null hypothesis. Retaining H0 is viewed as a weak decision and rejecting H0 is seen as a decision. The decision to retain Ho implies not that it is probably true, but that it could be true, whereas the decision to reject Ho implies that it is probably false and that H1 is probably true. This is not a serious problem, as most researchers ultimately hope to reject the null hypothesis. The research hypothesis is not tested directly because it lacks the necessary precision. A hypothesis must specify a single number about which the sampling distribution can be constructed. The null hypothesis meets this requirement. Furthermore, because the research hypothesis is identied with the alternative hypothesis, the decision to reject the null hypothesis will provide strong support for the research hypothesis. In a two-tailed or test, rejection regions are located in both tails of the sampling distribution, and the alternative hypothesis is concerned with a difference in the population mean in either direction. The difference could be either higher or lower. In a onetailed or test, the rejection region is located in just one tail of the sampling distribution. Therefore, the observed sample mean triggers the decision to reject the null hypothesis only if it differs in the specied direction. Before the hypothesis test is conducted, the researcher must decide whether to conduct a one or twotailed test and which direction (if onetailed) is signicant. The test is extra-sensitive. The level of signicance must also be chosen before the hypothesis test is conducted. The level of signicance equals the probability that even though the null hypothesis is true, an error could occur, and it could be rejected. Therefore, when the rejection of a true null hypothesis would have serious consequences, a smaller level of signicance would be appropriate. Alpha may be set to equal .01 or .001. The researcher chooses alpha and must do so before looking at the data. Section II 17