478 CHAPTER 9 Correlation and Regression Hypothesis Testing for a Population Correlation Coefficient R You can also use a hypothesis test to determine whether the sample correlation coefficient r provides enough evidence to conclude that the population correlation coefficient r is significant. A hypothesis test for r can be one-tailed or two-tailed. The null and alternative hypotheses for these tests are listed below. eH0: r Ú 0 (no significant negative correlation) Ha: r 6 0 (significant negative correlation) Left-tailed test eH0: r … 0 (no significant positive correlation) Ha: r 7 0 (significant positive correlation) Right-tailed test eH0: r = 0 (no significant correlation) Ha: r ≠0 (significant correlation) Two-tailed test In this text, you will consider only two-tailed hypothesis tests for r. A t@test can be used to test whether the correlation between two variables is significant. The test statistic is r and the standardized test statistic t = r sr = r B1 - r2 n - 2 follows a t@distribution with n - 2 degrees of freedom, where n is the number of pairs of data. (Note that there are n - 2 degrees of freedom because one degree of freedom is lost for each variable.) The t-Test for the Correlation Coefficient Using the t@Test for the Correlation Coefficient R In Words In Symbols 1. Identify the null and alternative hypotheses. State H0 and Ha. 2. Specify the level of significance. Identify a. 3. Identify the degrees of freedom. d.f. = n - 2 4. Determine the critical value(s) and Use Table 5 in the rejection region(s). Appendix B. 5. Find the standardized test statistic. t = r B1 - r2 n - 2 6. Make a decision to reject or fail to reject If t is in the rejection the null hypothesis. region, then reject H0. Otherwise, fail to reject H0. 7. Interpret the decision in the context of the original claim. GUIDELINES To use the t-test for a correlation coefficient, note that the requirements for calculating a correlation coefficient given on page 473 also apply to the test. In this text, unless stated otherwise, you can assume that these requirements are met.
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