550 CHAPTER 10 Chi-Square Tests and the F -Distribution 1 2 3 4 F F0 = 2.06 α= 0.10 Table 7 in Appendix B lists the critical values for the F@distribution for selected levels of significance a and degrees of freedom d.f.N and d.f.D. Finding Critical Values for the F@Distribution 1. Specify the level of significance a. 2. Determine the degrees of freedom for the numerator d.f.N. 3. Determine the degrees of freedom for the denominator d.f.D. 4. Use Table 7 in Appendix B to find the critical value. When the hypothesis test is a. one-tailed, use the a F@table. b. two-tailed, use the 1 2a F@table. Note that because F is always greater than or equal to 1, all one-tailed tests are right-tailed tests. For two-tailed tests, you need only to find the right-tailed critical value. GUIDELINES In Examples 1 and 2, the values of d.f.N and d.f.D are given. You will learn how to determine these values on page 552. Finding a Critical F@Value for a Right-Tailed Test Find the critical F@value for a right-tailed test when a = 0.10, d.f.N = 5, and d.f.D = 28. SOLUTION A portion of Table 7 is shown below. Using the a = 0.10 F@table with d.f.N = 5 and d.f.D = 28, you can find the critical value, as shown by the highlighted areas in the table. a 50.10 26 2.91 2.52 2.31 2.17 2.08 2.01 1.96 1.92 27 2.90 2.51 2.30 2.17 2.07 2.00 1.95 1.91 28 2.89 2.50 2.29 2.16 2.06 2.00 1.94 1.90 29 2.89 2.50 2.28 2.15 2.06 1.99 1.93 1.89 30 2.88 2.49 2.28 2.14 2.05 1.98 1.93 1.88 1 2 3 4 5 6 7 8 1 39.86 49.50 53.59 55.83 57.24 58.20 58.91 59.44 2 8.53 9.00 9.16 9.24 9.29 9.33 9.35 9.37 d.f.N: Degrees of freedom, numerator d.f.D: Degrees of freedom, denominator From the table, you can see that the critical value is F0 = 2.06. Critical value The figure at the left shows the F@distribution for a = 0.10, d.f.N = 5, d.f.D = 28, and F0 = 2.06. TRY IT YOURSELF 1 Find the critical F@value for a right-tailed test when a = 0.05, d.f.N = 8, and d.f.D = 20. Answer: Page A43 EXAMPLE 1
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