Bluman A.G. Elementary Statistics- A Step By Step Approach

Section 9–5 Testing the Difference Between Two Variances 515Figure 9–11 = 0.05Finding the CriticalValue in Table H forExample 9–12d.f.D.11d.f.N.2 ... 14 152... ...2021222.18As noted previously, when the F test is used, the larger variance is always placed inthe numerator of the formula. When you are conducting a two-tailed test, a is split; andeven though there are two values, only the right tail is used. The reason is that the F testvalue is always greater than or equal to 1.Example 9–13Find the critical value for a two-tailed F test with a 0.05 when the sample size fromwhich the variance for the numerator was obtained was 21 and the sample size from whichthe variance for the denominator was obtained was 12.SolutionSince this is a two-tailed test with a 0.05, the 0.052 0.025 table must be used.Here, d.f.N. 21 1 20, and d.f.D. 12 1 11; hence, the critical value is 3.23.See Figure 9–12.Figure 9–12 = 0.025Finding the CriticalValue in Table H forExample 9–13d.f.D.11d.f.N.2 ... 202... ...1011123.23When the degree of freedom values cannot be found in the table, the closest value onthe smaller side should be used. For example, if d.f.N. 14, this value is between thegiven table values of 12 and 15; therefore, 12 should be used, to be on the safe side.9–45