3 An analysis of variance experiment produced a portion of the accompanying ANOVA table. Assume normality in the underlying populations. (You may find it useful to reference the Etable.) picture Click here for the Excel Data File a. Specify the competing hypotheses in order to determine whether some differences exist between the population means. oped He: HA = HB " HC = PD; HA: Not all population means are equal. Book He: HA 2 HB 2 MC 2 up; HA: Not all population means are equal. Hint O Me: HA SUB S HC S HD; HA: Not all population means are equal. trences b. Fill in the missing statistics in the ANOVA table. (Round "MS" to 4 decimal places and "F' to 3 decimal places.) ANOVA Source of Variation SS MS F p-value Between Groups 18.97 0.0018 Within Groups 75.78 67 Total 94.75 70 c. At the 5% significance level, what is the conclusion to the test? Reject He; we can conclude that some means differ. O Do not reject He: we cannot conclude that some means differ. Do not reject He: we can conclude that some means differ. O Reject He; we cannot conclude that some means differ.Source of Variation SS df MS F p-value Between Groups 18.97 3 0.0018 Within Groups 75.78 67 Total 94.75 70TABLE 4 F Distribution Entries in this table provide the values of Fajay, 4) that correspond to a given upper-tail area a and a specified number of degrees of freedom in the numerator df, and degrees of freedom in the denominator df. For example, for a = 0.05, df, = 8, and df2 = 6. Area in Upper Tail, a P(F (x.) 2 4.15) = 0.05. of, 10 15 25 50 100 500 7 62.69 63.01 63.26 60.19 61.22 62.05 58.2 58.91 59.44 59.86 245.95 249.26 251.77 253.04 254.06 0.10 39.86 49.50 53.59 55.83 57.24 230.16 233.99 36.77 241.88 984.87 998.08 10 08 12 1013.17 1017.24 0.05 161.45 199.50 215.71 224.58 948.22 963.28 968.63 59.50 799.50 864.16 899.58 921.85 937.11 5858.99 5928.36 5981.07 6022.47 6055.85 6157.28 6239.83 6302.52 6334.11 647.79 0.01 4052.18 4999.50 5403.35 5624.58 5763.65 9.45 9.47 9.48 9.49 9.33 9.37 9.38 9.39 9.42 19.48 19.49 19.49 8.53 9.00 9.16 9.24 19.30 19.35 19.37 9.38 19.40 19.43 19.46 39.49 39.50 39.43 39.46 0.10 19.16 19.25 39.40 99.49 18.51 19.00 99.50 39.25 39.30 39.33 39.36 39.37 39.39 99.48 39.37 9.39 9.40 99.43 99.46 38.51 39.00 39.17 0.025 99.17 99.25 99.30 19.33 99.36 5.14 99.00 5.14 0.01 98.50 5.20 5.17 5.15 5.27 5.25 8.63 8.58 8.55 8.53 5.28 8.70 5.54 5.46 5.39 5.34 5.31 9.01 8.94 8.89 8.81 8.79 13.91 0.10 10.13 9.55 9.28 14.73 14.62 4.47 14.42 26.35 26.24 26.15 15.10 27.35 27.23 26.87 26.58 0.025 17.44 16.04 28.71 28.24 27.91 27.67 0.01 34.12 30.82 29.46 3.83 3.78 4.01 6.00 5.96 5.86 5.77 5.70 4.19 6.26 6.16 6.09 8.84 8.66 8.50 8.38 8.32 8.27 0.10 7.71 6.94 9.20 9.07 8.98 8.90 4.20 13.91 13.69 13.58 0.05 9.60 9.36 15.21 14.98 14.80 14.66 14.55 0.025 12.22 10.65 9.98 15.52 001 21.20 18.00 16.69 15.98 3.32 3.30 3.24 3.19 3.15 3.13 3.11 3.45 3.40 LEE 3.34 4.77 .62 1.52 4.41 4.37 3.62 6.03 4.06 3.78 3.52 5.19 4.88 6.43 6.27 6.08 0.10 6.14 0.05 6.61 5.79 5.41 7.39 7.15 6.98 6.85 6.68 6.62 0.05 9.72 9.45 9.13 9.04 0.025 10.0 8.43 7.76 10.46 10.16 12.06 11.39 10.97 10.67 10.29 0.01 16.26 13.27 2.81 2.77 2.75 3.68 3.29 3.18 3.05 3.01 2.98 2.96 3.83 5.11 4.86 0.10 5.52 5.27 6.99 6.90 0.05 5.99 5.14 5.70 5.60 7.09 6.60 6.23 5.99 5.82 798 7.56 7.30 0.025 8.81 7.26 8.10 10.92 9.78 9.15 8.75 8.47 8.26 13.75 2.50 3.27 3.24 4.16 3.07 4.40 5.59 4.35 4.76 4.28 4.21 0.10 3.87 6.62 5.86 5.67 0.05 5.52 6.06 5.75 0.025 8.07 6.54 5.89 9.55 8.45 7.85 2.35 2.32 2.30 12.25 2.94 2.67 3.02 2.97 2.73 w w in 3.81 3.74 3.68 0.10 3.46 3.11 2.92 2.81 4.07 3.69 507 1 96 4 88 0.05 5.32 4.46 0.025 7.57 6.06 5.47 5.05 4.82 7.59 7.01 6.63 6.18 691 2.17 0.01 11.26 8.65 2.44 2.42 2.76 3.18 3.36 5.12 4.2 3 86 3.6 4.72 5.26 471 452 4 41 0.05 535 4.96 7.21 5.71 5.08 5.47 8.02 6.99 6.42 6.06 5.61 10.56 2.17 2.09 2.73 2.64 2.52 3.09 10 0.10 3.29 2.92 3.15 3.71 3.48 3.33 3.72 3.52 3.35 3.22 3.93 0.05 4.96 4.31 4.12 4.01 0.025 6.94 5:46 4.83 4.47 4.24 4.07 3.95 001 10.04 7.56 6.55 5.99 5.64 2.01 2.25 2.17 2.10 2.04 1.98 2.60 2.42 2.39 2.27 2.51 2.46 2.90 0.10 3.23 2.86 2.66 2.54 2.45 2.90 3.16 303 2.96 4.84 3.59 3.20 3.59 3.62 4.04 4.0 281 3.71 4.28 4 74 463 0.025 6.72 5.26 4.63 5.67 5.32 4 89 1.91 0.01 9.65 721 6.22 2.24 2.21 2.0 .97 1.94 2.50 2.40 2.35 2.31 2.48 2.80 3.18 2.81 2.61 3.01 2.87 2.80 0.10 257 2 47 2 38 0.05 3.89 3.26 4.12 3.8 3.76 506 4.50 4 30 6.55 5.10 4.47 9.33 6.93 5.95 541 1.92 2.22 2.88 2.67 2.61 0.10 3.14 2.76 4 67 3.81 3.41 3.18 3.03 3.25 3.27 0.05 4.97 4.35 4.00 3.77 3.60 3.57 6:41 0.025 5.21 1.80 9.07 6.70 5.74 2.12 1.93 1.87 1.83 2.52 2.65 2.24 2.39 2.31 2.24 2.6 2.56 2.50 0.10 3.10 2.73 0.05 3.74 3.21 4.60 3.34 322 311 3.03 3.89 3.66 403 0.025 6.30 4.86 4.24 8 86 4 69 6.51 5.56 5.04 1.89 1.83 2.1 2.08 2.47 2.41 0.10 3.07 2.70 2.49 2.69 2.55 2 89 0.05 3.68 3.29 3.06 2.90 3.80 3.58 380 3.52 3.28 308 298 6.20 4.77 4.15 4.00 5.42 4.89 4 56 1.73 8.68 6.36 2.06 1.79 2.23 2.12 2.07 2.02 2.40 2.33 0.10 3.05 2.67 2.33 2.47 0.05 4.49 3.63 3.24 3.01 2.85 2.61 g w - 6 3.50 3.16 297 286 6.12 4.69 4.08 3.73 0.025 4.77 4.44 8.53 6.23 5.29 1.76 1.73 1.69 2.03 2.0 2.02 1.97 3.03 2.64 2.44 2.31 2.22 2.4 2.33 2.26 0.10 0.05 4.45 3.59 3.20 287 276 2.68 20 0.025 6.04 4.62 4.01 0.01 6.11 A 67 1.67 1.80 2.04 2.00 1.93 2.14 3.01 2.62 2.42 2.29 2.20 2.5 2.46 2.27 U.TO 2.49 2.3 2.20 259 4.41 3.55 3.16 2.93 2.98 2.78 268 0.05 4.56 3.95 3.61 3.38 3.71 3.60 3.51 3.23 0.025 5.98 6.01 5.09 4.58 4.25 4.01 0.01 8.29 1.94 wig 2.00 2.44 2.30 2.22 2.15 0.10 2.9% 2.61 2.90 2.88 2.82 2.62 3.52 271 0.05 5.92 4.51 3.90 3.56 3.33 352 343 291 0.025 5.01 4.50 4.17 001 8.18 5.93 1.69 1.65 1.62 8 2.16 1.96 1.76 2.25 2.07 1.97 1.91 1.86 2.97 2.59 2.38 2.17 20 0.10 4.35 3.49 3.10 2.87 2.7 2.84 2.77 2.40 2.20 2.54 0.05 4.46 3.86 3.51 3.29 3.01 2.46 2 37 28 0.025 5.87 210 4.94 4.43 4.10 1.60 1.83 236 2.21 0.10 3.47 2.84 258 2.48 0.05 5.83 4.42 3.82 3.51 340 3.31 2.79 3.81 8.02 5.78 4.87 4.37 1.65 1.61 1.80 wig 2.0 1.91 2.17 2.02 0.10 2.35 2.32 2.09 2.95 4.30 3.44 3.05 2.82 2.73 253 2.42 0.05 5 79 4.38 3.78 3.44 3.22 0.025 001 7.95 5.72 4.82 4.31 1.95 1.92 1.71 1.64 1.59 1.56 2.00 1.88 1.82 1.77 2.94 2.55 2.34 2.21 2.11 0.10 2.29 2.14 2.06 1.99 2.37 2.28 4.28 3.42 3.03 3.41 3.18 321 2.69 248 0.025 4.35 3.75 5.75 5.66 4.26 394 0.01 1.70 1.62 1.58 1.97 1.86 1.80 175 wip 2.93 2.54 301 2.19 2.26 2.02 in co 4.26 0.025 5.72 4.32 3.72 3.26 2.64 2.33 0.05 3.40 3.38 3.90 1.53 0.01 7.82 5.61 4.72 1.87 1.77 1.68 1.61 1.56 1.96 1.84 1.78 1.73 1.92 0.10 2.92 2.53 2.32 2.09 2.02 2.23 2.08 2.00 0.05 4.24 3.39 2.99 2.76 3.13 2.97 2.40 219 0.025 4.29 3.69 001 7.77 5.57 4.68 4.18 1.67 1.59 1.55 1.51 1.82 1.76 1.71 1.9 1.90 0.10 2.91 2.52 2.31 2.17 2.01 2.05 2.98 2.7 2.59 2.39 2.21 236 2 25 216 4.23 3.37 3.33 3.10 3.09 2.81 2.57 0.025 5.66 4.27 3.67 414 3.82 5.53 1.66 1.58 1-54 1.50 7.72 1.91 1.87 1.9 1.81 1.74 2.25 1.87 2.90 2.51 2.30 2.17 2.07 2.31 2.7 2.57 2.36 2.18 2.03 1.94 2.96 2.33 2.22 212 W co win 4.21 3.35 4.24 3.65 3.31 3.08 3.15 3.06 2.78 2.54 0.025 5.63 4.11 3.78 001 7.68 5.49 4.60 1.57 1.53 1.49 1.75 1.67 1.91 1.73 1.92 1.85 0.10 2.89 2.50 2.29 2.16 201 2.09 0.05 4.20 3.34 2.95 2.71 2.55 1 8 8 219 4.22 3.63 3.29 3.06 3.03 2.51 2.30 0.025 3.75 601 7.64 5.45 4.57 4.07 1.56 1.52 1.77 1.71 1.65 1.99 1.90 1.83 0.10 0.05 4.18 3.33 2.93 2.70 327 2.16 206 4.20 3.27 3.04 3.20 209 200 2.73 0.025 5.59 3.61 373 0.01 5.42 4.04 1.5 1.47 1.85 1.76 1.64 2.49 2.28 2.14 1.97 005 3.32 2.92 2.6 2.45 2.25 213 203 0.05 4.17 2.70 4.18 3.59 3.25 307 298 5.39 451 4.02 3.70 3.47 7.56 1.60 1.92 1.75 1.56 1.57 0.10 2.81 2.79 256 2.38 2.32 1 95 171 0.05 3.18 0.025 5.34 3.97 3.39 3.05 2.83 001 7.17 5.06 4.20 3.72 1.29 1.23 2.00 1.91 1.78 1.56 1.48 1.39 1.31 2.14 1.7 7 1.59 1.48 1.38 100 0.10 2.76 2.36 3.94 2.70 2.46 2.31 2.32 0.05 2.92 2.70 2.59 1.97 1.74 1.60 1.47 0.025 5.18 3.83 3.25 2.69 3.51 3.21 0.01 6.90 3.98 1 28 WIN 2.31 500 3 86 3.01 2.62 2.39 1.23 0.05 2.59 2.07 1.57 5.05 3.72 3.14 2.81 3.82 3.36 3.05 2.84 2.68 2.55 2.36 6.69 4.65 ource: F-values calculated with Excel