Mathematical Methods for Physics and Engineering - Matematica.NET

31.7 HYPOTHESIS TESTINGC n1 ,n 2(F) n 1 = 1 2 3 4 5 6 7 8n 2 =1 161 200 216 225 230 234 237 2392 18.5 19.0 19.2 19.2 19.3 19.3 19.4 19.43 10.1 9.55 9.28 9.12 9.01 8.94 8.89 8.854 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.045 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.826 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.157 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.738 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.449 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.2310 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.0720 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.4530 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.2740 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.1850 4.03 3.18 2.79 2.56 2.40 2.29 2.20 2.13100 3.94 3.09 2.70 2.46 2.31 2.19 2.10 2.03∞ 3.84 3.00 2.60 2.37 2.21 2.10 2.01 1.94n 1 = 9 10 20 30 40 50 100 ∞n 2 =1 241 242 248 250 251 252 253 2542 19.4 19.4 19.4 19.5 19.5 19.5 19.5 19.53 8.81 8.79 8.66 8.62 8.59 8.58 8.55 8.534 6.00 5.96 5.80 5.75 5.72 5.70 5.66 5.635 4.77 4.74 4.56 4.50 4.46 4.44 4.41 4.376 4.10 4.06 3.87 3.81 3.77 3.75 3.71 3.677 3.68 3.64 3.44 3.38 3.34 3.32 3.27 3.238 3.39 3.35 3.15 3.08 3.04 3.02 2.97 2.939 3.18 3.14 2.94 2.86 2.83 2.80 2.76 2.7110 3.02 2.98 2.77 2.70 2.66 2.64 2.59 2.5420 2.39 2.35 2.12 2.04 1.99 1.97 1.91 1.8430 2.21 2.16 1.93 2.69 1.79 1.76 1.70 1.6240 2.12 2.08 1.84 1.74 1.69 1.66 1.59 1.5150 2.07 2.03 1.78 1.69 1.63 1.60 1.52 1.44100 1.97 1.93 1.68 1.57 1.52 1.48 1.39 1.28∞ 1.88 1.83 1.57 1.46 1.39 1.35 1.24 1.00Table 31.4 Values of F for which the cumulative probability function C n1 ,n 2(F)of the F-distribution with (n 1 ,n 2 ) degrees of freedom has the value 0.95. Forexample, for n 1 =10andn 2 =6,C n1 ,n 2(4.06) = 0.95.customary to define the rejection region on F as F>F crit ,whereC n1,n 2(F crit )=∫ Fcrit1P (F|H 0 ) dF = α,and n 1 = N 1 − 1 and n 2 = N 2 − 1 are the numbers of degrees of freedom.Table 31.4 lists values of F crit corresponding to the 5% significance level (i.e.α =0.05) for various values of n 1 and n 2 .1295