Question: TABLE 4 F DISTRIBUTION Area or probability 0 Fa Entries in the table give F values, where a is the area or probability in

TABLE 4 F DISTRIBUTION Area or probability 0 Fa Entries in the table give F values, where a is the area or probability in the upper tail of the F distribution. For example, with 4 numerator degrees of freedom, 8 denominator degrees of freedom, and a .05 area in the upper tail, F05 = 3.84. 1 2 3 4 5 6 7 8 Numerator Degrees of Freedom 9 10 15 20 25 30 40 60 100 1000 9.37 9.38 19.37 19.38 9.39 19.40 39.37 39.39 39.40 99.38 99.39 99.40 5.25 5.24 5.23 8.85 14.54 8.81 8.79 14.47 14.42 27.49 27.34 27.23 3.95 3.94 3.92 6.04 6.00 5.96 8.98 8.90 8.84 14.80 14.66 14.55 3.34 3.32 3.30 4.82 4.77 4.74 6.76 6.68 6.62 10.29 10.16 10.05 2.98 2.96 4.15 5.60 4.10 4.06 5.52 5.46 8.10 7.98 7.87 2.75 2.72 3.68 4.10 3.73 4.90 6.84 2.59 3.44 4.43 6.03 2.47 3.23 4.82 6.72 2.56 3.39 4.36 5.91 2.44 3.18 4.03 2.54 3.35 4.30 5.81 2.42 3.14 3.96 3.51 4.57 6.31 2.70 3.64 4.76 5.47 5.35 5.26 2.38 2.35 2.32 3.07 3.85 3.02 3.78 2.98 3.72 5.06 4.94 4.85 2.30 2.27 2.25 2.95 2.90 3.66 3.59 2.85 3.53 4.74 4.63 4.54 2.24 2.21 2.19 2.85 3.51 2.80 3.44 2.75 3.37 4.50 4.39 4.30 2.20 2.16 2.14 2.77 2.71 3.39 3.31 2.67 3.25 4.30 4.19 4.10 2.15 2.12 2.10 2.70 2.65 3.29 3.21 2.60 3.15 4.14 4.03 3.94 2.12 2.09 2.06 2.64 3.20 2.59 2.54 3.12 3.06 4.00 3.89 3.80 2.09 2.06 2.03 2.59 3.12 2.54 2.49 3.05 2.99 3.89 3.78 3.69 2.06 2.03 2.00 2.55 3.06 2.49 2.45 2.98 2.92 3.79 3.68 3.59 2.04 2.00 1.98 2.51 2.46 2.41 3.01 2.93 2.87 3.71 3.60 3.51 2.02 1.98 1.96 2.48 2.42 2.38 2.96 2.88 2.82 3.63 3.52 3.43 2.00 1.96 1.94 2.45 2.39 2.35 2.91 2.84 2.77 3.56 3.46 3.37 1.98 1.95 1.92 2.42 2.87 2.37 2.32 2.80 2.73 3.51 3.40 3.31 1.97 1.93 1.90 2.40 2.34 2.30 2.84 2.76 2.70 3.45 3.35 3.26 1.95 1.92 1.89 2.37 2.32 2.27 2.81 2.73 2.67 3.41 3.30 3.21 1.94 1.91 1.88 2.36 2.30 2.25 2.78 3.36 2.70 3.26 2.64 3.17 1.93 1.89 1.87 2.34 2.75 2.28 2.24 2.68 2.61 3.32 3.22 3.13 1.92 2.32 2.73 3.29 1.91 2.31 2.71 3.26 1.90 2.29 2.69 3.23 1.89 2.28 2.67 3.20 1.88 2.27 2.65 3.17 1.83 2.18 2.53 2.99 1.77 2.10 2.41 2.82 **** **** *** *888 355 434 4306 1.88 1.86 2.27 2.22 2.65 2.59 3.18 3.09 1.87 1.85 2.25 2.20 2.63 2.57 3.15 3.06 1.87 1.84 2.24 2.19 2.61 2.55 3.12 3.03 1.86 1.83 2.22 2.18 2.59 2.53 3.09 3.00 1.85 1.82 2.21 2.16 2.57 2.51 3.07 2.98 1.79 1.76 2.12 2.08 2.45 2.39 2.89 2.80 1.74 1.71 2.04 1.99 2.33 2.27 2.72 2.63 1.73 1.69 1.66 2.03 2.32 2.69 1.97 2.24 2.59 1.93 2.18 2.50 1.68 1.64 1.61 1.95 2.20 1.89 2.13 1.84 2.06 2.53 2.43 2.34 **** **** , **** *** ***** ***************** **** ** ** ** **** ** ** ** ** ** ** **** * ** ** ** 9530 4933 , , * *** *** **** ** **** *** *** GAA AAA 543 5509 9403 **** *** ** ** **** **** **** **** **** **** *** *** *** **** *88 89 9438 9.42 9.44 99.43 99.45 238.88 240.54 245.95 248.02 59.44 59.86 60.19 241.88 61.22 61.74 62.05 62.26 62.53 62.79 249.26 250.10 251.14 252.20 998.09 956.64 963.28 968.63 984.87 993.08 254.19 1001.40 1005.60 1009.79 1013.16 1017.76 6286.43 6312.97 6333.92 6362.80 5980.95 6022.40 6055.93 6156.97 6208.66 6239.86 6260.35 19.43 39.43 19.45 39.45 9.47 19.47 19.48 39.48 99.48 9.49 19.49 39.50 9.45 19.46 39.46 9.46 19.46 39.46 9.47 99.46 99.47 39.47 99.48 5.20 5.18 5.17 5.17 5.16 5.15 8.70 14.25 8.66 8.63 8.62 8.59 8.57 14.17 14.12 14.08 14.04 13.99 26.87 26.69 26.58 26.50 26.41 26.32 3.87 3.84 3.83 3.82 3.80 3.79 5.86 5.80 5.77 5.75 5.72 5.69 8.66 8.56 8.50 8.46 8.41 8.36 14.20 14.02 13.91 13.84 13.75 13.65 3.324 3.21 4.62 4.56 6.43 6.33 9.72 9.55 2.87 3.94 2.84 3.87 5.27 5.17 7.56 7.40 2.63 2.59 3.44 4.47 6.16 2.46 2.42 3.22 4.10 3.15 4.00 5.52 5.36 2.34 2.30 3.01 3.77 4.96 2.94 3.67 4.81 2.24 2.20 2.85 2.77 3.52 3.42 4.56 2.17 2.72 3.33 4.25 4.41 2.12 2.65 3.23 4.10 2.10 2.06 2.62 2.54 3.18 3.07 4.01 3.86 3.19 3.17 3.16 3.14 4.52 4.50 4.46 4.43 6.27 6.23 6.18 6.12 9.45 9.38 9.29 9.20 2.81 2.80 2.78 2.76 3.83 3.81 3.77 3.74 5.11 5.07 5.01 4.96 7.30 7.23 7.14 7.06 2.57 2.56 2.54 2.51 3.40 3.38 3.34 3.30 4.40 4.36 4.31 4.25 6.06 5.99 5.91 5.82 2.40 2.38 2.36 2.34 3.11 3.08 3.04 3.01 3.94 3.89 3.84 3.78 5.26 5.20 5.12 5.03 2.27 2.25 2.23 2.21 2.89 2.86 2.83 2.79 3.60 3.56 3.51 3.45 4.71 4.65 4.57 4.48 2.17 2.16 2.13 2.11 2.73 2.70 2.66 2.62 3.35 3.31 3.26 3.20 4.31 4.25 4.17 4.08 2.10 2.08 2.05 2.03 2.60 2.57 2.53 2.49 3.16 3.12 3.06 3.00 4.01 3.94 3.86 3.78 2.03 2.01 1.99 1.96 2.50 2.47 2.43 2.38 3.01 2.96 2.91 2.85 3.76 3.70 3.62 3.54 2.05 2.01 1.98 1.96 1.93 1.90 2.53 3.05 3.82 2.01 2.46 2.46 2.95 2.41 2.38 2.34 2.30 2.88 2.84 2.78 2.72 3.66 3.57 3.51 3.43 3.34 1.96 1.93 1.99 1.89 1.86 2.39 2.34 2.31 2.27 2.22 2.95 2.84 2.78 2.73 2.67 2.61 3.66 3.51 3.41 3.35 3.27 3.18 1.97 1.92 1.89 1.87 1.85 1.82 2.40 2.33 2.28 2.25 2.20 2.16 2.86 2.76 2.69 2.64 2.59 2.52 3.52 3.37 3.28 3.21 3.13 3.05 1.94 1.89 2.35 2.79 2.28 2.68 3.41 3.26 1.91 1.86 2.31 2.23 2.72 2.62 3.31 3.16 1.89 1.84 2.27 2.19 2.67 2.56 3.23 3.08 1.86 1.81 2.23 2.16 2.62 2.51 3.15 3.00 1.86 1.84 1.81 1.78 2.23 2.19 2.15 2.11 2.61 2.57 2.51 2.45 3.16 3.10 3.02 2.93 1.83 1.81 1.78 1.75 2.18 2.15 2.10 2.06 2.55 2.50 2.44 2.38 3.07 3.00 2.92 2.83 1.80 1.78 1.75 1.72 2.14 2.11 2.06 2.02 2.49 2.44 2.38 2.32 2.98 2.92 2.84 2.75 1.78 1.76 1.73 1.70 2.11 2.07 2.03 1.98 2.44 2.39 2.33 2.27 2.91 2.84 2.76 2.67 1.84 1.79 1.76 1.74 1.71 1.68 2.20 2.12 2.07 2.04 1.99 1.95 2.57 3.09 2.46 2.94 2.40 2.35 2.29 2.22 2.84 2.78 2.69 2.61 1.83 1.78 1.74 1.72 1.69 1.66 2.18 2.53 2.10 2.42 2.05 2.01 1.96 1.92 2.36 2.31 2.25 2.18 3.03 2.88 2.79 2.72 2.64 2.55 1.81 1.76 1.73 1.70 1.67 1.64 2.15 2.07 2.02 1.98 1.94 1.89 2.50 2.39 2.32 2.27 2.21 2.14 2.98 2.83 2.73 2.67 2.58 2.50 1.80 1.74 1.71 1.69 1.66 1.62 2.13 2.47 2.05 2.36 2.00 1.96 1.91 1.86 2.29 2.24 2.18 2.11 2.93 2.78 2.69 2.62 2.54 2.45 1.78 1.73 2.11 2.44 2.03 2.33 2.89 2.74 1.77 1.72 2.09 2.01 2.41 2.30 2.85 2.70 1.76 1.71 2.07 1.99 2.39 2.28 2.81 2.66 1.75 1.70 2.06 1.97 2.36 2.25 2.78 2.63 1.74 1.69 2.04 2.34 1.96 2.23 2.75 2.60 1.73 1.68 2.03 1.94 2.32 2.21 2.73 2.57 1.72 1.67 2.01 2.31 1.93 2.20 2.70 2.55 1.66 1.61 1.92 1.84 2.18 2.07 2.52 2.37 1.60 1.54 1.84 2.06 1.75 1.94 2.35 2.20 1.56 1.49 1.77 1.68 1.97 1.85 2.22 2.07 1.49 1.68 1.85 1.43 1.58 1.72 2.06 1.90 , **6* 1.70 1.67 1.64 1.61 1.97 1.94 1.89 1.84 2.26 2.21 2.15 2.08 2.64 2.58 2.49 2.40 1.68 1.66 1.96 1.92 1.63 1.87 1.59 1.82 2.23 2.18 2.12 2.05 2.60 2.54 2.45 2.36 1.67 1.65 1.61 1.58 1.94 1.90 1.85 1.80 2.21 2.16 2.09 2.03 2.57 2.50 2.42 2.33 1.66 1.64 1.60 1.57 1.92 1.88 1.84 1.79 2.18 2.13 2.07 2.00 2.54 2.47 2.38 2.29 1.65 1.63 1.59 1.56 1.91 1.87 1.82 1.77 2.16 2.11 2.05 1.98 2.51 2.44 2.35 2.26 1.64 1.62 1.58 1.55 1.89 1.85 1.81 1.75 2.14 2.09 2.03 1.96 2.48 2.41 2.33 2.23 1.61 1.84 1.57 1.79 1.54 1.74 2.07 2.45 2.39 2.01 2.30 1.94 2.21 1.57 1.54 1.78 1.74 1.51 1.69 1.47 1.64 1.99 1.94 1.88 1.80 2.27 2.20 2.11 2.02 1.50 1.48 1.44 1.40 1.69 1.65 1.59 1.53 1.87 1.82 1.74 1.67 2.10 2.03 1.94 1.84 1.45 1.42 1.38 1.34 1.62 1.57 1.52 1.45 1.77 1.71 1.64 1.56 1.97 1.89 1.80 1.69 1.38 1.35 1.30 1.25 1.52 1.47 1.41 1.33 1.64 1.58 1.50 1.41 1.79 1.72 1.61 1.50 63.30 99.50 5.14 5.13 8.53 13.91 26.14 3.76 5.63 8.26 13.47 3.13 3.11 4.37 6.02 9.03 2.72 3.67 4.86 6.89 2.47 3.23 4.15 5.66 2.30 2.93 3.68 4.87 2.16 2.71 3.34 4.32 2.06 2.54 3.09 3.92 1.98 2.41 2.96 2.89 3.61 1.91 2.30 2.73 3.37 1.85 2.21 2.60 3.18 1.80 2.14 2.50 3.02 1.76 2.07 2.40 2.88 1.72 2.02 2.32 2.76 1.69 1.97 2.26 2.66 1.66 1.92 2.20 2.58 1.64 1.88 2.14 2.50 1.61 1.85 2.09 2.43 1.59 1.82 2.05 2.37 1.57 1.79 2.01 2.32 1.55 1.76 1.98 2.27 1.54 1.74 1.94 2.22 1.52 1.72 1.91 2.18 1.51 1.70 1.89 2.14 1.50 1.68 1.86 2.11 1.48 1.66 1.84 2.08 1.47 1.65 1.82 2.05 1.46 1.63 1.80 2.02 1.38 1.52 1.65 1.82 1.30 1.40 1.49 1.62 1.22 1.30 1.36 1.45 1.08 1.11 1.13 1.16 4.53 6.23 9.15 2.96 4.12 5.99 8.75 2.88 3.97 5.82 8.47 2.83 3.87 , , , , 2.53 3.02 , 2.51 2.99 3.67 2.49 2.97 3.63 2.01 2.47 2.94 3.59 2.00 2.46 2.92 2.42 2.87 2.34 2.74 , , , 3.99 2.11 2.05 2.64 3.18 3.15 3.13 , 4.87 2.35 4.82 2.34 2.84 3.48 4.37 2.22 2.82 3.44 4.31 2.21 2.80 3.25 4.04 2.13 2.66 3.22 3.09 3.81 2.06 2.55 3.05 3.76 39.86 161.45 647.79 4052.18 8.53 18.51 38.51 98.50 5.54 10.13 17.44 34.12 4.54 7.71 12.22 21.20 4.06 6.61 10.01 16.26 3.78 5.99 8.81 13.75 3.59 5.59 8.07 12.25 3.46 5.32 7.57 11.26 3.36 5.12 7.21 10.56 3.29 4.96 6.94 10.04 3.23 4.84 6.72 53.59 215.71 864.15 5403.53 9.16 19.16 39.17 99.16 5.39 9.28 15.44 29.46 4.19 6.59 9.98 16.69 3.62 5.41 7.76 12.06 3.29 4.76 55.83 224.58 57.24 230.16 899.60 921.83 5624.26 5763.96 9.24 19.25 39.25 99.25 5.34 9.12 15.10 28.71 4.11 6.39 9.60 15.98 3.52 5.19 7.39 11.39 9.29 19.30 39.30 99.30 5.31 9.01 14.88 28.24 4.05 6.26 9.36 15.52 3.45 5.05 7.15 10.97 3.11 4.39 58.20 233.99 937.11 5858.95 9.33 19.33 39.33 99.33 5.28 8.94 14.73 27.91 4.01 6.16 9.20 15.21 3.40 4.95 6.98 10.67 3.05 4.28 5.89 8.45 2.92 4.07 5.42 7.59 2.81 3.86 5.08 6.99 2.73 3.71 4.83 6.55 2.66 3.59 4.63 6.22 2.61 3.49 4.47 5.95 2.56 3.41 4.35 5.74 2.52 3.34 4.24 5.56 2.49 3.29 4.15 5.42 2.46 3.24 4.08 5.29 2.44 3.20 4.01 5.19 2.42 5.52 7.85 2.81 3.84 5.05 7.01 2.69 3.63 4.72 6.42 2.61 3.48 4.47 5.99 2.54 3.36 4.28 5.67 2.48 3.26 4.12 5.41 2.43 3.18 4.00 5.21 2.39 3.11 3.89 5.04 2.36 3.06 3.80 4.89 2.33 3.01 3.73 4.77 2.31 2.96 3.66 4.67 2.29 2.93 3.61 5.29 7.46 2.73 3.69 4.82 6.63 2.61 3.48 4.48 6.06 2.52 3.33 4.24 5.64 2.45 3.20 4.04 5.32 2.39 3.11 3.89 5.06 2.35 3.03 3.77 4.86 2.31 2.96 3.66 4.69 2.27 2.90 3.58 4.56 2.24 2.85 3.50 4.44 2.22 2.81 3.44 4.34 2.20 2.77 3.38 3.16 3.95 5.09 4.58 4.25 2.40 2.27 3.13 3.90 5.01 2.90 3.56 4.50 2.25 2.87 3.51 4.43 2.18 2.74 3.33 4.17 2.16 2.71 3.29 5.12 7.19 2.67 3.58 4.65 6.37 2.55 3.37 4.32 5.80 2.46 3.22 4.07 5.39 2.39 3.09 3.88 5.07 2.33 3.00 3.73 4.82 2.28 2.92 3.60 4.62 2.24 2.85 3.50 4.46 2.21 2.79 3.41 4.32 2.18 2.74 3.34 4.20 2.15 2.70 3.28 4.10 2.13 2.66 3.22 4.01 2.11 2.63 3.17 3.94 2.09 2.60 3.13 2.38 3.10 3.86 4.94 4.10 3.87 2.36 2.23 2.14 2.08 3.07 2.68 2.57 3.82 6.60 9.78 3.07 4.35 3.05 3.78 3.03 3.75 4.76 3.94 3.71 2.33 2.19 2.10 2.04 3.01 2.62 3.72 4.72 4.22 3.90 2.32 2.18 2.09 2.02 2.99 2.60 3.41 4.26 2.78 3.38 , 2.76 3.35 3.69 2.59 3.10 2.57 4.18 3.85 2.31 2.08 2.98 3.67 4.64 4.14 3.82 2.30 2.17 2.07 2.96 3.65 4.68 2.17 2.74 3.33 2.73 3.31 3.08 2.71 3.29 4.07 2.15 2.70 3.27 4.04 3.06 3.75 2.06 2.55 3.04 2.45 2.90 3.53 1.99 2.43 2.88 4.11 3.78 3.56 2.29 2.16 2.06 2.00 2.95 2.56 3.63 4.57 2.28 2.93 4.60 3.03 2.90 2.37 2.79 3.34 1.91 1.85 3.34 4.13 2.14 3.98 2.09 3.01 3.65 2.00 2.46 2.92 3.51 1.95 2.38 2.80 3.34 2.31 2.70 3.21 2.22 2.58 3.04 1.87 2.25 2.63 3.12 1.83 2.19 2.54 2.99 1.78 2.11 2.42 2.82 3.61 4.54 3.73 3.50 2.28 2.14 2.05 1.98 2.92 2.53 3.59 4.51 4.02 3.70 3.47 2.23 2.09 2.00 1.93 2.84 2.45 3.46 4.31 3.83 3.51 3.29 2.18 2.04 1.95 2.76 2.69 3.25 2.61 3.13 2.53 2.70 3.25 2.61 3.13 3.80 , **************** *** *** **** **** **** **** *** ** ** ** ** 999 39 ** **** **** **** **** **** **** 3045 3598 533 33 383 38** **** **** 5889 , , , 3.18 4.75 6.55 9.33 3.14 4.67 6.41 9.07 3.10 4.60 6.30 8.86 3.07 4.54 6.20 8.68 3.05 4.49 6.12 8.53 3.03 4.45 6.04 8.40 3.01 4.41 5.98 8.29 2.99 4.38 5.92 8.18 2.97 4.35 5.87 8.10 2.96 4.32 5.83 8.02 2.95 4.30 5.79 7.95 2.94 4.28 5.75 7.88 2.93 4.26 5.72 7.82 2.92 4.24 5.69 7.77 2.91 4.23 5.66 7.72 2.90 4.21 5.63 7.68 2.89 4.20 5.61 7.64 2.89 4.18 5.59 7.60 2.88 4.17 5.57 7.56 2.84 4.08 5.42 7.31 2.79 4.00 *** 5.29 7.08 2.76 3.94 5.18 6.90 2.71 3.85 5.04 6.66 = 8 Denominator Degrees of Freedom Area in 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 21 22 23 24 25 26 27 28 29 30 30 40 60 100 1000 11.2 Practice 2. Consider the following hypothesis test. Ho: = H : 00 Ha a = 8.4, n = 26, and 8 = 4. Use = 0.05 and the p-value approach. s a. What is your conclusion if n = 21, s n2 Calculate the value of the test statistic (to 2 decimals). The p-value is - Select your answer What is your conclusion? - Select your answer- . Use Table 4 of Appendix B. b. Repeat the test using the critical value approach. What is the rejection rule for this hypothesis test? Round the critical values to 2 decimal places. Reject Ho if F - Select your answer - What is your conclusion? - Select your answer-

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