A survey looked at the value of recreational sports on college campuses. One of
ID: 3056305 • Letter: A
Question
A survey looked at the value of recreational sports on college campuses. One of the questions asked each student to rate the importance of recreational sports to college satisfaction and success. Responses were on a 10-point scale with 1 indicating total lack of importance and 10 indicating very high importance. The following table summarizes these results:
(a) To compare the mean scores across classes, what are the degrees of freedom for the ANOVA F statistic?
(b) The MSG = 11.506. If sp = 2.12, what is the F statistic? (Round your answer to two decimal places.)
F =
(c) Give an approximate (from Table E) or exact (from software) P-value. (Enter your answer to four decimal places.)
Sophomore
Junior
Senior 728
536
594
438 7.6
7.6
7.5
7.3 Probability p Table entry for p is the critical value F* with probability p lying to its right. F critical values Degrees of freedom in the numerator 56 100 .050 1.025 .010 001 | 39.86 161.45 647.79 4052.2 405284 | 49.50 199.50 799.50 4999.5 500000 53.59 215.71 864.16 5403.4 540379 55.83 | 224.58 899.58 5624.6 562500 57.24 230.16 1921.85 5763.6 576405 58.20 233.99 1937.11 5859.0 585937 58.91 236.77 948.22 5928.4 592873 59.44 238.88 1956.66 5981.1 598144 59.86 240.54 963.28 6022.5 602284 100 1050 1025 2010 001 8.53 | 18.51 38.51 98.50 998.50 9.00 19.00 39.00 99.00 999.00 19.16 19.16 39.17 9.17 999.17 9.24 19.25 39.25 9.25 999.25 9.29 19.30 39.30 99.30 999.30 9.33 19.33 39.33 99.33 999.33 9.35 19.35 39.36 99.36 999.36 9.37 19.37 39.37 9.37 999.37 9.38 19.38 39.39 99.39 999.39 100 1050 025 15.54 | 10.13 17.44 34.12 167.03 5.46 19.55 16.04 30.82 148.50 5.39 9.28 15.44 29.46 14111 5.34 19.12 15.10 28.71 137.10 5.31 9.01 14.88 28.24 134.58 5.28 8.94 14.73 27.91 132.85 5.27 8.89 14.62 27.67 131.58 5.25 8.85 14.54 27.49 130.62 5.24 8.81 14.47 27.35 129.86 2010 001 100 1050 Degrees of freedom in the denominator .025 4.54 17.71 12.22 21.20 74.14 4.32 6.94 10.65 18.00 61.25 4.19 6.39 9.98 16.69 56.18 4.11 6.39 9.60 15.98 53.44 4.05 6.26 9.36 15.52 51.71 4.01 6.16 9.20 15.21 50.53 3.98 6.09 9.07 14.98 9.66 3.95 6.04 8.98 14.80 49.00 3.94 6.00 8.90 14.66 48.47 .010 001 Lun 100 .050 .025 .010 1001 4.06 6.61 10.01 16.26 47.18 3.78 5.79 8.43 13.27 37.12 3.62 5.41 7.76 12.06 33.20 3.52 5.19 7.39 11.39 31.09 3.45 5.05 17.15 10.97 29.75 3.40 4.95 16.98 10.67 28.83 3.37 4.88 6.85 10.46 28.16 3.34 4.82 [6.76 10.29 27.65 3.32 4.77 6.68 10.16 27.24 .100 1050 1.025 2010 1001 3.78 5.99 18.81 13.75 3.46 5.14 7.26 10.92 27.00 3.29 4.76 6.60 9.78 23.70 3.18 4.53 6.23 9.15 21.92 3.11 4.39 5.99 8.75 20.80 3.05 4.28 5.82 8.47 20.03 3.01 4.21 5.70 8.26 19.46 2.98 4.15 5.60 8.10 19.03 2.96 4.10 5.52 7.98 18.69 35.51 .100 1050 .025 2010 001 3.59 5.59 8.07 12.25 29.25 3.26 4.74 6.54 9.55 21.9 3.07 4.35 5.89 8.45 18.77 2.96 4.12 5.52 7.85 17.20 2.88 3.97 5.29 7.46 16.21 2.83 3.87 5.12 7.19 15.52 2.78 3.79 4.99 6.99 15.02 2.75 3.73 4.90 6.84 14.63 2.72 3.68 4.82 6.72 1433 Probability P Table entry for p is the critical value F* with probability plying to its right. Fcritical values (continued) Degrees of freedom in the numerator | 10 12 15 2015 30 40 50 60 120 1000 60.19 241.88 968.63 6055.8 605621 60.71 243.91 1976.71 6106.3 610668 61.22 245.95 984.87 6157.3 615764 61.74 62.05 248.01 249.26 1993.10 | 998.08 62087 6239.8 620908 624017 62.26 62.53 250.1025114 | 1001.4 1005.6 6260.6 6286.8 626099 628712 62.69 251.77 | 1008.1 6302.5 630285 62.79 252.20 | 1009.8 6313.0 631337 63.06 253.25 | 1014.0 6339.4 633972 63.30 254.19 1017.7 6362.7 636301 9.39 19.40 39.40 9.40 999.40 19.41 19.41 39.41 99.42 999.42 9.42 19.43 39.43 9.43 999.43 9.44 19.45 39.45 9.45 999.45 9.45 19.46 39.46 99.46 999.46 9.46 19.46 39.46 9.47 999.47 9.47 19.47 39.47 9.47 999.47 9.47 19.48 39.48 99.48 999.48 19.47 19.48 39.48 99.48 999.48 9.48 19.49 39.49 9.49 999.49 9.49 19.49 39.50 99.50 999.50 5.20 8.70 5.23 8.79 14.42 27.23 12925 5.22 8.74 14.34 27.05 128.32 5.18 18.66 14.17 26.9 126.42 5.17 8.63 14.12 14.25 5.17 8.62 14.08 26.50 125.45 5.16 8.59 14.04 26.41 124.96 5.15 8.58 14.01 26.35 124.66 5.15 8.57 13.99 26.32 124.47 5.14 8.55 13.95 26.22 123.97 5.13 8.53 13.91 26.14 123.53 26.58 26.87 127.37 125.84 3.92 5.96 18.84 14.55 48.05 3.90 5.91 18.75 14.37 47.41 3.87 5.86 18.66 14.20 46.76 3.84 5.80 8.56 14.02 46.10 3.83 5.77 8.50 13.91 45.70 3.82 5.75 8.46 13.84 45.43 3.80 5.72 18.41 13.75 45.09 3.80 5.70 18.38 13.69 4.88 3.79 5.69 8.36 13.65 44.75 3.78 5.66 8.31 13.56 44.40 3.76 5.63 18.26 13.47 44.09 3.30 4.74 6.62 10.05 26.92 3.27 4.68 6.52 9.89 26.42 3.24 4.62 6.43 9.72 25.91 3.21 4.56 6.33 9.55 25.39 3.19 452 6.27 9.45 25.08 3.17 4.50 6.23 9.38 24.87 3.16 4.46 6.18 19.29 24.60 3.15 4.44 6.14 9.24 24.4 3.14 4.43 6.12 9.20 24.33 3.12 4.40 6.07 9.11 24.06 3.11 4.37 6.02 9.03 23.82 2.94 4.06 5.46 7.87 18.41 2.90 4.00 5.37 7.72 17.99 2.87 3.94 5.27 756 17.56 2.84 3.87 5.17 7.40 17.12 2.81 3.83 5.11 7.30 16.85 2.80 3.81 5.07 7.23 16.67 2.78 3.77 5.01 7.14 16.44 2.77 3.75 4.98 7.09 16.31 2.76 3.74 4.96 7.06 16.21 2.74 3.70 4.90 6.97 15.98 2.72 3.67 4.86 6.89 15.77 2.70 3.64 4.76 6.62 14.08 2.67 3.57 4.67 6.47 13.71 2.63 3.51 47 6.31 13.32 259 3.44 4.47 6.16 12.93 2.57 3.40 4.40 6.06 12.69 2.56 3.38 4.36 5.99 12.53 2.54 3.34 4.31 5.91 12.33 2.52 3.32 4.28 5.86 1120 2.51 3.30 4.25 5.82 12.12 2.49 3.27 4.20 5.74 11.91 2.47 3.23 4.15 15.66 11.72 (Corettilited) Fcritical values (continued) Forritical values (continued) Degrees of freedom in the numerator 100 1050 1.025 2010 1001 3.46 5.32 7.57 11.26 25.41 3.11 4.46 6.06 8.65 18.49 292 4.07 5.42 7.59 15.83 2.81 3.84 5.05 7.01 14.39 2.73 3.69 4.82 6.63 13.48 2.67 3.58 4.65 6.37 12.86 2.62 3.50 4.53 6.18 12.40 2.59 3.44 4.43 6.03 12.05 2.56 3.39 4.36 5.91 11.77 1100 1050 2025 1010 2001 3.36 5.12 7.21 10.56 22.86 3.01 4.26 5.71 8.02 16.39 2.81 3.86 5.08 6.99 13.90 2.69 3.63 4.72 6.42 12.56 2.61 3.48 4.48 6.06 11.71 2.55 3.37 4.32 5.80 11.13 2.51 3.29 4.20 5.61 10.70 2.47 3.23 4.10 547 10.37 2.44 3.18 4.03 5.35 1011 1100 1050 2025 2010 001 3.29 4.96 6.94 10.04 21.04 2.92 4.10 5.46 756 14.91 2.73 3.71 4.83 6.55 1255 2.61 3.48 4.47 5.99 11.28 2.52 3.33 4.24 5.64 10.48 2.46 3.22 4.07 3.39 9.93 2.41 3.14 3.95 5.20 9.52 2.38 3.07 3.85 5.06 920 2.35 3.02 3.78 494 8.96 2.27 1100 1050 025 2010 2001 3.23 4.84 6.72 9.65 19.69 2.86 3.98 5.26 7.21 13.81 2.66 3.59 4.63 2.54 3.36 4.28 5.67 10.35 2.45 3.20 4.04 5.32 9.58 2.39 3.09 3.88 5.07 9.05 234 3.01 3.76 4.89 8.66 2.30 2.95 3.66 4.74 8.35 2.90 3.59 4.63 8.12 6.22 11.56 100 1050 2025 1010 1001 Degrees of freedom in the denominator 3.18 4.75 6.55 9.33 18.64 2.81 3.89 5.10 6.93 12.97 2.61 3.49 4.47 5.95 10.80 2.48 3.26 4.12 5.41 9.63 2.39 3.11 3.89 5.06 8.89 2.33 3.00 3.73 4.82 8.38 2.28 2.91 3.61 4.64 8.00 2.24 2.85 3.51 4.50 7.71 2.21 2.80 3.44 4.39 7.48 u 100 1050 1025 010 1001 3.14 4.67 6.41 9.07 17.82 2.76 3.81 4.97 6.70 12.31 2.56 3.41 4.35 5.74 1021 2.43 3.18 4.00 5.21 9.07 2.35 3.03 3.77 4.86 8.35 2.28 2.92 3.60 4.62 7.86 2.23 2.83 3.48 4.44 7.49 2.20 2.77 3.39 4.30 7.21 2.16 2.71 3.31 4.19 6.98 4 1100 1050 2025 2010 2001 3.10 4.60 6.30 8.86 17.14 2.73 3.74 4.86 6.51 11.78 2.52 3.34 4.24 5.56 9.73 2.39 3.11 3.89 5.04 8.62 2.31 2.96 3.66 4.69 792 2.24 2.85 3.50 4.46 7.44 2.19 2.76 3.38 4.28 7.08 2.15 2.70 3.29 4.14 6.80 2.12 2.65 3.21 4.03 6.58 100 1050 1025 2010 1001 3.07 4.54 6.20 8.68 16.59 2.70 3.68 4.77 6.36 11.34 2.49 3.29 4.15 5.42 9.34 2.36 3.06 3.80 4.89 8.25 2.27 2.90 3.58 4.56 7.57 2.21 2.79 3.41 4.32 7.09 2.16 2.71 3.29 4.14 6.74 2.12 2.64 3.20 4.00 6.47 2.09 2.59 3.12 3.89 6.26 2.09 2.59 1100 1050 025 1010 001 3.05 4.49 6.12 8.53 16.12 2.67 3.63 4.69 6.23 10.97 2.46 3.24 4.08 5.29 9.01 2.33 3.01 3.73 4.77 7.94 2.24 2.85 3.50 4.44 7.27 2.18 2.74 3.34 420 6.80 2.13 2.66 3.22 4.03 6.46 3.12 3.89 6.19 2.06 2.54 3.05 3.78 5.98 100 050 2025 2010 2001 3.03 4.45 6.04 8.40 15.72 2.64 3.59 4.62 6.11 10.66 2.44 3.20 4.01 5.19 8.73 2.31 2.96 3.66 4.67 7.68 2.22 2.81 3.44 4.34 7.02 2.15 2.70 3.28 4.10 6.56 2.10 2.61 3.16 3.93 6.22 2.06 2.55 3.06 3.79 5.96 2.03 2.49 2.98 3.68 5.75 Fcritical values (continued) Degrees of freedom in the numerator 10 12 15 20 25 30 40 50 60 120 1000 2.4 3.35 4.30 5.81 11.54 2.50 3.28 4.20 5.67 11.19 2.46 3.22 4.10 5.52 10.84 2.42 3.15 4.00 5.36 10.48 2.40 3.11 3.94 5.26 10.26 2.38 3.08 3.89 5.20 10.11 2.36 3.04 3.84 5.12 9.92 2.35 3.02 3.81 5.07 9.80 2.34 3.01 3.78 5.03 9.73 2.32 2.97 3.73 4.95 9.53 2.30 2.93 3.68 4.87 9.36 2.42 3.14 3.96 5.26 9.89 2.38 3.07 3.87 5.11 9.57 2.34 3.01 3.77 4.96 9.24 2.30 2.94 3.67 4.81 8.90 2.27 2.89 3.60 4.71 8.69 2.25 2.86 3.56 4.65 8.55 2.23 2.83 3.51 4.57 8.37 2.22 2.80 3.47 4.52 8.26 2.21 2.79 3.45 4.48 8.19 2.18 2.75 3.39 4.40 8.00 2.16 271 3.34 4.32 7.84 2.32 2.98 3.72 4.85 8.75 2.28 2.91 3.62 4.71 8.45 2.24 2.85 3.52 4.56 2.20 2.77 3.42 2.17 2.73 3.35 4.31 7.60 2.16 270 3.31 4.25 7.47 2.13 2.66 3.26 4.17 7.30 2.12 2.64 3.22 4.12 7.19 2.11 2.62 3.20 4.08 7.12 2.08 2.58 3.14 4.00 6.94 2.06 2.54 3.09 3.92 6.78 4.41 8.13 7.80 2.25 2.85 3.53 4.54 7.92 2.21 2.79 3.43 4.40 7.63 2.17 2.72 3.33 4.25 7.32 2.12 2.65 3.23 4.10 7.01 2.10 2.60 3.16 4.01 6.81 2.08 2.57 3.12 3.94 6.68 2.05 2.53 3.06 3.86 652 2.04 2.51 3.03 3.81 6.42 2.03 2.49 3.00 3.78 6.35 2.00 2.45 2.94 3.69 6.18 1.98 2.41 2.89 3.61 6.02 2.19 2.75 3.37 4.30 7.29 2.15 2.69 3.28 4.16 7.00 2.10 2.62 3.18 4.01 6.71 2.06 2.54 3.07 3.86 6.40 2.03 2.50 3.01 3.76 6.22 2.01 2.47 2.96 3.70 6.09 1.99 2.43 2.91 3.62 5.93 1.97 2.40 2.87 3.57 5.83 1.96 2.38 2.85 3.54 5.76 1.93 2.34 2.79 3.45 5.59 191 2.30 2.73 3.37 5.44 2.14 2.67 3.25 4.10 6.80 1.96 2.38 2.10 2.60 3.15 3.96 6.52 2.05 2.53 3.05 3.82 6.23 2.01 2.46 2.95 3.66 1.98 2.41 2.88 3.57 5.75 2.84 1.93 2.34 2.78 3.43 5.47 1.92 2.31 2.74 3.38 537 1.90 2.30 2.72 3.34 5.30 1.88 2.25 2.66 3.25 5.14 1.85 2.21 2.60 3.18 4.99 3.51 5.63 5.93 2.10 2.60 3.15 3.94 6.40 2.05 253 3.05 3.80 6.13 2.01 2.46 2.95 3.66 5.85 1.96 2.39 2.84 1.93 2.34 2.78 3.41 5.38 1.91 2.31 2.73 3.35 5.25 1.89 2.27 2.67 3.27 5.10 1.87 2.24 2.64 3.22 5.00 1.86 2.22 2.61 3.18 4.94 1.83 2.18 2.55 3.09 4.77 1.80 2.14 2.50 3.02 4.62 3.51 5.56 1.89 2.28 2.06 254 3.06 3.80 6.08 2.02 2.48 2.96 3.67 5.81 1.97 2.40 2.86 3.52 5.54 1.92 2.33 2.76 3.37 5.25 2.69 3.28 5.07 187 2.25 2.64 321 4.95 1.85 220 2.59 3.13 4.80 1.83 2.18 2.55 3.08 4.70 1.82 2.16 2.52 3.05 4.64 1.79 2.11 2.46 2.96 4.47 1.76 2.07 2.40 2.88 433 1.12 2.03 2.49 299 3.69 5.81 1.99 2.42 2.89 3.55 5.55 1.94 2.35 2.79 341 5.27 1.89 2.28 2.68 3.26 4.99 1.86 2.23 2.61 3.16 4.82 1.84 2.19 2.57 3.10 4.70 1.81 2.15 251 3.02 4.54 1.79 2.12 2.47 2.97 4.45 1.78 2.11 2.45 2.93 4.39 1.75 2.06 2.38 2.84 423 2.02 232 2.76 4.08 2.00 2.45 2.92 3.39 5.58 1.96 2.38 2.82 3.46 5.32 1.91 231 2.72 3.31 5.05 1.86 2.23 2.62 3.16 4.78 1.83 2.18 2.55 3.07 4.60 181 2.15 2.50 3.00 4.48 1.78 2.10 2.44 2.92 4.33 1.76 2.08 2.41 2.87 4.24 1.75 2.06 2.38 2.83 4.18 1.72 2.01 2.32 2.75 1.69 1.97 2.26 2.66 3.87 4.02 (Confireled) Fcritical values (continued) Degrees of freedom in the numerator 12345 78 100 1050 1025 1010 3.01 4.41 5.98 8.29 15.38 2.62 3.55 4.56 6.01 10.39 2.42 3.16 3.95 5.09 8.49 2.29 2.93 3.61 4.58 7.46 2.20 2.77 3.38 4.25 6.81 2.13 2.66 3.22 4.01 6.35 2.08 2.58 3.10 3.84 6.02 2.04 2.51 3.01 3.71 5.76 2.00 2.46 2.93 3.60 5.56 4001 100 .050 .025 1010 1001 2.99 4.38 5.92 8.18 15.08 2.61 3.52 4.51 5.93 10.16 2.40 3.13 3.90 5.01 8.28 2.27 2.90 3.56 4.50 7.27 218 2.74 3.33 211 2.63 3.17 3.94 6.18 2.06 2.54 3.05 3.77 5.85 2.02 2.48 2.96 3.63 5.59 1.98 2.42 2.88 3.52 5.39 4.17 6.62 100 1050 1025 2010 2001 2.97 4.35 5.87 8.10 14.82 2.59 3.49 4.46 5.85 9.95 2.38 3.10 3.86 4.94 8.10 2.25 2.87 3.51 4.43 710 2.16 2.71 3.29 4.10 6.46 2.09 2.60 3.13 3.87 6.02 2.04 251 3.01 3.70 5.69 2.00 2.45 2.91 3.56 5.44 1.96 2.39 2.84 3.46 5.24 1100 1.050 1025 .010 1001 2.96 4.32 5.83 8.02 14.59 2.57 3.47 4.42 5.78 9.77 2.36 3.07 3.82 4.87 7.94 2.23 2.84 3.48 4.37 6.95 2.14 2.68 3.25 4.04 6.32 2.08 2.57 3.09 3.81 5.88 2.02 2.49 2.97 3.64 5.56 1.98 2.42 2.87 1.95 2.37 2.80 3.40 5.11 3.51 5.31 2.13 2.66 100 .050 .025 010 1001 2.95 4.30 5.79 7.95 14.38 256 3.44 4.38 5.72 9.61 Degrees of freedom in the denominator 2.35 3.05 3.78 4.82 7.80 2.22 2.82 3.44 4.31 6.81 3.22 2.06 2.55 3.05 3.76 5.76 2.01 2.46 2.93 3.59 5.44 1.97 2.40 2.84 3.45 193 2.34 2.76 3.35 4.99 3.99 6.19 5.19 .100 050 1025 .010 .001 2.94 4.28 5.75 7.88 14.20 2.55 3.42 4.35 5.66 9.47 2.34 3.03 3.75 4.76 7.67 2.21 2.80 3.41 4.26 6.70 2.11 2.64 3.18 3.94 6.08 2.05 2.53 3.02 3.71 5.65 1.99 2.44 2.90 3.54 5.33 1.95 2.37 2.81 3.41 5.09 1.92 2.32 2.73 3.30 4.89 1.91 2.30 100 1050 1025 2010 2.93 4.26 5.72 7.82 14.03 2.54 3.40 4.32 5.61 9.34 2.33 3.01 3.72 4.72 7.55 2.19 2.78 3.38 4.22 6.59 2.10 2.62 3.15 3.90 5.98 2.04 2.51 2.99 3.67 5.55 1.98 2.42 2.87 3.50 1.94 236 2.78 3.36 4.99 2.70 3.26 4.80 4001 5.23 100 1050 1.025 2010 1001 2.92 4.24 5.69 777 13.88 2.53 3.39 4.29 5.57 9.22 2.32 2.99 3.69 4.68 7.45 2.18 2.76 3.35 4.18 6.49 2.09 2.60 3.13 3.85 5.89 2.02 2.49 2.97 3.63 5.46 1.97 2.40 2.85 3.46 5.15 1.93 2.34 2.75 3.32 4.91 1.89 2.28 2.68 3.22 4.71 252 3.37 100 1050 .025 .010 .001 2.91 4.23 5.66 7.72 13.74 4.27 5.53 9.12 2.31 2.98 3.67 4.4 7.36 2.17 2.74 3.33 4.14 6.41 2.08 2.59 3.10 3.82 5.80 2.01 2.47 2.94 3.59 5.38 1.96 2.39 2.82 3.42 5.07 1.92 2.32 2.73 3.29 4.83 1.88 2.27 2.65 3.18 4.64 1.87 1100 1050 1025 010 1001 2.25 2.90 4.21 5.63 7.68 13.61 2.51 3.35 4.24 2.30 2.96 3.65 4.60 7.27 2.17 2.73 3.31 4.11 6.33 2.07 2.57 3.08 3.78 5.73 2.00 2.46 2.92 3.56 5.31 1.95 2.37 2.80 339 5.00 1.91 2.31 2.71 3.26 4.76 5.49 2.63 3.15 4.57 9.02 Fcritical values (continued) Degrees of freedom in the numerator | 10 12 1520 20 10 12 25 30 40 50 60 120 50 120 40 60 1000 1.98 2.41 2.87 3.51 5.39 1.93 234 2.77 3.37 5.13 1.89 2.27 2.67 3.23 4.87 1.84 2.19 2.56 3.08 459 1.80 2.14 2.49 2.98 4.42 1.78 2.11 2.44 292 4.30 175 2.06 2.38 2.84 4.15 1.74 2.04 2.35 2.78 4.06 1.72 2.02 2.32 2.75 4.00 1.69 1.97 2.26 2.66 3.84 1.66 192 2.20 2.58 3.69 1.91 2.31 1.96 2.38 2.82 3.43 5.22 2.72 1.86 2.23 2.62 3.15 4.70 1.81 2.16 2.51 3.00 4.43 1.78 2.11 2.44 2.91 4.26 176 2.07 2.39 2.84 4.14 1.73 2.03 2.33 2.76 3.99 171 2.00 2.30 2.71 3.90 1.70 1.98 2.27 2.67 3.84 1.67 1.93 2.20 2.58 3.68 1.64 1.88 2.14 2.50 3.53 3.30 4.97 1.94 235 2.77 3.37 5.08 1.89 2.28 2.68 3.23 4.82 1.84 2.20 2.57 3.09 4.56 1.79 2.12 2.46 2.94 4.29 1.76 2.07 2.40 2.84 4.12 174 2.04 2.35 2.78 4.00 1.71 1.99 229 2.69 3.86 1.69 1.97 2.25 2.64 3.77 1.68 1.95 222 2.61 3.70 1.64 1.90 2.16 252 3.54 1.61 1.85 2.09 2.43 3.40 1.92 2.32 2.73 3.31 4.95 1.87 2.25 2.64 3.17 4.70 1.83 2.18 253 3.03 4.4 1.78 2.10 2.42 2.8 4.17 1.74 2.05 2.36 2.79 4.00 1.72 2.01 2.31 2.72 3.88 1.9 1.96 2.25 2.64 3.74 1.67 1.94 2.21 2.58 3.64 1.66 1.92 2.18 2.55 3.58 1.62 1.87 2.11 2.46 3.42 1.59 1.82 2.05 2.37 3.28 1.76 1.90 2.30 2.70 3.26 4.83 186 2.23 2.60 3.12 4.58 1.81 2.15 2.50 2.98 4.33 2.07 239 2.83 4.06 1.73 2.02 2.32 2.73 3.89 1.70 1.98 2.27 2.67 3.78 1.67 1.94 2.21 2.58 3.63 1.65 1.91 2.17 2.53 3.54 1.64 1.89 2.14 2.50 3.48 1.60 1.84 2.08 2.40 3.32 1.57 179 2.01 2.32 3.17 1.64 1.88 1.89 2.27 2.67 3.21 473 1.84 2.20 257 3.07 4.48 1.80 2.13 2.47 2.93 4.23 1.74 2.05 2.36 2.78 3.96 1.71 2.00 2.29 2.69 1.69 1.96 2.24 2.62 3.68 1.66 1.91 2.18 2.54 3.53 2.14 1.62 1.86 211 2.45 3.38 1.59 1.81 2.04 2.35 3.22 1.55 176 1.98 2.27 3.08 3.79 2.48 3.44 1.88 2.25 2.64 3.17 4.64 1.83 2.18 2.54 3.03 4.39 1.78 2.11 2.4 2.89 4.14 1.73 203 2.33 2.74 3.87 1.70 1.97 2.26 2.64 3.71 1.67 1.94 2.21 2.58 3.59 1.64 1.89 2.15 2.49 3.45 1.62 1.86 2.11 2.44 3.36 1.61 1.84 2.08 2.40 3.29 1.57 1.79 2.01 2.31 3.14 14 174 1.94 2.22 2.99 1.87 2.24 2.61 3.13 4.56 1.82 2.16 2.51 2.99 4.31 1.77 2.09 2.41 2.85 4.06 1.72 2.01 2.30 2.70 3.79 1.68 1.96 2.23 2.60 3.63 1.66 1.92 2.18 254 3.52 1.63 1.87 2.12 2.45 3.37 1.61 1.84 2.08 2.40 3.28 1.59 1.82 2.05 2.36 3.22 1.56 1.77 1.98 127 3.06 152 172 1.91 2.18 2.91 1.86 2.22 2.59 3.09 4.48 1.81 2.15 2.49 2.96 4.24 1.76 2.07 2.39 2.81 3.99 1.71 1.99 2.28 2.66 3.72 1.67 1.94 2.21 2.57 3.56 1.65 1.90 2.16 250 3.44 1.61 1.85 2.09 2.42 3.30 1.39 1.82 2.05 2.36 3.21 158 1.80 2.03 2.33 3.15 154 1.75 1.95 2.23 2.99 151 1.70 1.89 2.14 2.84 1.85 2.20 2.57 3.06 4.41 1.80 2.13 2.47 2.93 4.17 1.75 2.06 2.36 178 3.92 1.70 1.97 2.25 2.63 3.66 1.66 1.92 2.18 254 3.49 1.64 1.88 2.13 2.47 3.38 1.60 1.84 2.07 238 3.23 1.58 1.81 2.03 233 3.14 157 179 2.00 2.29 3.08 153 173 1.93 220 292 1.50 1.68 1.86 2.11 2.78 (Cottinated) F critical values (continued) Degrees of freedom in the numerator 34 2.50 3.34 1.87 2.24 28 100 1050 1025 .010 1001 2.89 4.20 5.61 7.64 13.50 4.22 2.29 2.95 3.63 4.57 7.19 2.16 2.71 3.29 4.07 6.25 2.06 2.56 3.06 3.75 5.66 2.00 2.45 2.90 3.53 5.24 1.94 2.36 2.78 3.36 4.93 1.90 2.29 2.69 3.23 4.69 2.61 5.45 8.93 3.12 4.50 1100 050 1025 .010 .001 2.89 4.18 5.59 7.60 13.39 2.50 3.33 4.20 5.42 8.85 2.28 2.93 3.61 4.54 7.12 2.15 2.70 3.27 4.04 6.19 2.06 2.55 3.04 3.73 5.59 1.99 2.43 2.88 3.50 5.18 1.93 2.35 2.76 3.33 4.87 1.89 2.28 2.67 3.20 4.64 1.86 2.22 2.59 3.09 4.45 30 100 1050 1025 .010 .001 2.88 4.17 5.57 7.56 13.29 2.49 3.32 4.18 5.39 8.77 2.28 2.92 3.59 4.51 7.05 2.14 2.69 3.25 4.02 6.12 2.05 2.53 3.03 3.70 5.53 1.98 2.42 2.87 3.47 5.12 1.93 2.33 2.75 3.30 4.82 1.88 2.27 2.65 3.17 4.58 1.85 2.21 2.57 3.07 4.39 1.79 2.12 40 100 1050 025 010 1001 2.84 4.08 5.42 7.31 12.61 2.44 3.23 4.05 5.18 8.25 2.23 2.84 3.46 4.31 6.59 2.09 2.61 3.13 3.83 5.70 2.00 2.45 2.90 3.51 5.13 1.93 234 2.74 3.29 4.73 1.87 2.25 2.62 3.12 4.4 1.83 2.18 2.53 2.99 4.21 2.45 2.89 4.02 Degrees of freedom in the denominator 100 050 1025 .010 .001 2.81 4.03 5.34 7.17 12.22 2.41 3.18 3.97 5.06 7.9% 2.20 2.79 3.39 4.20 6.34 2.06 2.56 3.05 3.72 5.46 1.97 2.40 2.83 3.41 4.90 1.90 2.29 2.67 3.19 4.51 1.84 120 2.55 3.02 4.22 1.80 2.13 2.46 2.89 4.00 1.76 2.07 2.38 2.78 3.82 1.82 2.17 60 1100 1050 1.025 .010 001 2.79 4.00 5.29 7.08 11.97 2.39 3.15 3.93 4.98 7.77 2.18 2.76 3.34 4.13 6.17 2.04 2.53 3.01 3.65 5.31 1.95 2.37 2.79 3.34 476 1.87 2.25 2.63 3.12 4.37 2.51 1.77 2.10 2.41 2.82 3.86 1.74 2.04 2.33 2.72 3.69 2.95 4.09 100 100 1050 1025 .010 001 2.76 3.94 5.18 6.90 11.50 2.36 3.09 3.83 4.82 7.41 2.14 2.70 3.25 3.98 5.86 2.00 2.46 2.92 3.51 5.02 191 2.31 2.70 3.21 4.48 1.83 2.19 2.54 2.99 4.11 1.78 2.10 2.42 2.82 3.83 1.73 2.03 2.32 2.69 3.61 1.69 1.97 2.24 2.59 3.44 200 100 1050 1025 1010 001 2.73 3.89 5.10 6.76 11.15 2.33 3.04 3.76 4.71 715 2.11 2.65 3.18 3.88 5.63 1.97 2.42 2.85 3.41 4.81 1.88 2.26 2.63 3.11 4.29 1.80 2.14 2.47 2.89 3.92 1.75 2.06 2.35 2.73 3.65 1.70 1.98 2.26 2.60 3.43 1.66 193 2.18 2.50 3.26 1000 100 1050 1025 .010 1001 2.71 3.85 5.04 6.66 10.89 231 3.00 3.70 4.63 6.96 2.09 2.61 3.13 3.80 5.46 1.95 2.38 2.80 3.34 4.65 1.85 2.22 2.58 3.04 4.14 1.78 2.11 2.42 2.82 3.78 1.72 2.02 2.30 2.66 3.51 1.68 1.95 2.20 2.53 3.30 1.64 1.89 2.13 2.43 3.13 Fritical values (continued) Degrees of freedom in the numerator 10 12 15 20 25 50 60 120 1000 1.84 2.19 2.55 3.03 435 1.79 2.12 2.45 2.90 4.11 1.74 2.04 2.34 2.75 3.86 1.69 1.96 2.23 2.60 3.60 1.65 1.91 2.16 2.51 3.43 1.63 1.87 2.11 2.44 3.32 1.59 1.82 2.05 2.35 3.18 157 179 2.01 2.30 3.09 156 177 1.98 2.26 3.02 152 171 1.91 2.17 2.86 1.48 1.66 1.84 2.08 2.72 13 1.62 1.85 1.83 2.18 2.53 3.00 4.29 1.78 2.10 2.43 2.87 4.05 2.03 2.32 2.73 3.80 1.68 1.94 2.21 257 3.54 1.64 1.89 2.14 2.48 3.38 2.09 2.41 3.27 1.58 1.81 2.03 2.33 3.12 156 177 199 2.27 3.03 1.55 1.75 196 2.23 2.97 151 1.70 1.89 2.14 2.81 1.47 1.65 1.82 2.05 2.66 1.82 2.16 251 2.98 4.24 1.77 2.09 2.41 2.84 4.00 1.72 2.01 231 2.70 3.75 1.67 1.93 2.20 2.55 3.49 1.63 1.88 2.12 2.45 3.33 1.61 1.84 2.07 2.39 3.22 1.57 1.79 2.01 2.30 3.07 1.55 1.76 1.97 2.25 2.98 1.54 1.74 194 2.21 2.92 1.50 1.68 1.87 2.11 2.76 1.46 1.63 1.80 2.02 2.61 1.76 2.08 2.39 2.80 3.87 1.71 2.00 2.29 2.66 3.64 1.66 1.92 2.18 2.52 3.40 1.61 1.84 2.07 2.37 3.14 1.57 1.78 1.99 2.27 2.98 154 1.74 1.94 2.20 2.87 1.51 1.69 1.88 211 2.73 1.48 1.66 1.83 2.06 2.64 1.47 1.64 1.80 2.02 2.57 1.42 1.58 172 1.92 2.41 1.38 1.52 1.65 1.82 2.25 1.73 2.03 2.32 2.70 3.67 1.68 1.95 2.22 2.56 3.4 1.63 1.87 2.11 2.42 3.20 1.57 1.78 1.99 2.27 295 1.53 173 1.92 2.17 279 1.50 19 1.87 2.10 2.68 1.46 1.63 1.80 2.01 2.53 1.44 1.60 175 195 2.44 1.42 158 1.72 191 2.38 138 151 1.64 1.80 2.21 1.33 1.45 156 1.70 2.05 1.71 1.99 2.27 2.63 3.54 1.66 1.92 2.17 2.50 3.32 1.60 1.84 2.06 2.35 3.08 1.54 1.75 1.94 2.20 2.83 150 1.69 1.87 2.10 2.67 1.48 1.65 1.82 2.03 2.55 1.44 159 1.74 1.4 2.41 1.41 156 170 1.88 2.32 1.40 153 1.67 1.84 2.25 1.35 1.47 1.58 173 2.08 1.30 1.40 1.49 1.62 1.92 1.66 1.93 2.18 2.50 3.30 1.61 1.85 2.08 2.37 3.07 1.56 1.77 1.97 2.22 2.84 1.49 1.68 1.85 2.07 2.59 1.45 1.62 177 1.97 2.43 1.42 157 1.71 1.89 2.32 1.38 152 1.64 1.80 2.17 135 1.48 159 1.74 2.08 1.34 1.45 156 1.69 2.01 128 138 1.46 157 1.83 1.22 1.30 1.36 1.45 1.64 1.16 1.21 1.63 1.88 2.11 2.41 3.12 1.58 1.80 2.01 2.27 2.90 1.52 1.72 1.90 2.13 2.67 1.46 1.62 1.78 197 2.42 1.41 156 170 1.87 2.26 1.38 152 1.64 179 2.15 1.34 1.46 156 1.69 2.00 131 141 151 1.63 1.90 1.29 119 1.47 1.58 1.83 1.23 130 1.37 1.45 1.64 1.25 1.30 1.43 1.61 1.84 2.06 2.34 2.99 1.55 1.76 1.96 2.20 2.77 1.49 1.68 1.85 2.06 2.54 1.43 1.58 1.72 1.90 2.30 1.38 1.52 1.64 1.79 2.14 1.35 1.47 1.58 1.72 2.02 1.30 1.41 1.50 1.6] 1.87 127 1.36 1.45 154 177 1.25 1.33 1.41 150 1.69 118 1.24 1.29 1.35 149 1.08 1.11 1.13 1.16 1.22
Explanation / Answer
from given data:
1)numerator df =4-1 =3
denomiantor df =728+536+594+438-4 =2292
b)
MSE =sp2 =2.122 =4..4944
hence F =MSG/MSE =11.506/4.4944 =2.56
c) for above df and test statistic p value =0.0534
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