SECTION 10.3 Comparing Two Variances 551 When performing a two-tailed hypothesis test using the F@distribution, you need only to find the right-tailed critical value. You must, however, remember to use the 1 2a F@table. Finding a Critical F@Value for a Two-Tailed Test Find the critical F@value for a two-tailed test when a = 0.05, d.f.N = 4, and d.f.D = 8. SOLUTION A portion of Table 7 is shown below. Using the 1 2 a = 1 210.052 = 0.025 F@table with d.f.N = 4 and d.f.D = 8, you can find the critical value, as shown by the highlighted areas in the table. a 50.025 1 2 3 4 5 6 7 8 1 647.8 799.5 864.2 899.6 921.8 937.1 948.2 956.7 2 38.51 39.00 39.17 39.25 39.30 39.33 39.36 39.37 3 17.44 16.04 15.44 15.10 14.88 14.73 14.62 14.54 4 12.22 10.65 9.98 9.60 9.36 9.20 9.07 8.98 5 10.01 8.43 7.76 7.39 7.15 6.98 6.85 6.76 6 8.81 7.26 6.60 6.23 5.99 5.82 5.70 5.60 7 8.07 6.54 5.89 5.52 5.29 5.12 4.99 4.90 8 7.57 6.06 5.42 5.05 4.82 4.65 4.53 4.43 9 7.21 5.71 5.08 4.72 4.48 4.32 4.20 4.10 d.f.N: Degrees of freedom, numerator d.f.D: Degrees of freedom, denominator From the table, the critical value is F0 = 5.05. Critical value The figure shows the F@distribution for 1 2a = 0.025, d.f.N = 4, d.f.D = 8, and F0 = 5.05. 1 2 3 4 5 6 F F0 = 5.05 α= 0.025 1 2 TRY IT YOURSELF 2 Find the critical F@value for a two-tailed test when a = 0.01, d.f.N = 2, and d.f.D = 5. Answer: Page A43 EXAMPLE 2 Study Tip When using Table 7 in Appendix B to find a critical value, you will notice that some of the values for d.f.N or d.f.D are not included in the table. If the number you need for d.f.N or d.f.D is exactly midway between two values in the table, then use the critical value midway between the corresponding critical values. In some cases, though, it is easier to use technology to calculate the P@value, compare it to the level of significance, and then decide whether to reject the null hypothesis.
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