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Sample Consider the data in the table collected from four independent populations. The conclusion of a one-way ANOVA test using a=0.05 is that the population means are not all the same. Determine which means are different using a = 0.05. Sample 1 5 6 3 8 Sample 2 12 14 16 Bokea 21 13 15 24 Sample 4 10 3 11 Click here to view the ANOVA summary table. Click here to view a table of critical values for the studentized range. Х Let Xq, X2, X3, and 4 be the means for samples 1, 2, 3, and 4, respectively. Find the absolute values of the differences between the means. X1-x2= |x2-x3= |, -X31 = 0 *2-44] = 0 Summary table of the ANOVA results |«9- 48 -x | = | (Type integers or decimals. Do not round.) Sum of Degrees of Mean Sum of Find the Tukey-Kramer critical range CR for each of these differences. Source Squares Freedom Squares Between 381.75 127.25 CR12 = CR23 = Within 137.75 10 13.775 CR1,3 = CR24 = 0 519.5 13 CR 4 = CR34 = (Round to two decimal places as needed.) F 9.238 Total State the conclusions about the means for a = 0.05. Print Done different different different Since X1 - 2 Since IX, - Xz Since X-X4 Since - Xa Since x2 - 4 Since *3 = x V CR1.2, conclude that the means for samples 1 and 2 V CR1.3, conclude that the means for samples 1 and 3 CR14, conclude that the means for samples 1 and 4 V CR23, conclude that the means for samples 2 and 3 CR24, conclude that the means for samples 2 and 4 V CR34, conclude that the means for samples 3 and 4 different. different different

2 3 3 5 6 7 8 9 10 Dz 2 D2 1 17.97 26.98 37.08 40.41 45.40 47.36 49.07 1 2 10.88 13.03 6.09 4.50 2 8.33 5.91 38.32 9.80 6.82 5.76 43.12 12.44 8.48 11.74 8.04 13.54 9.18 13.99 9.46 3 7.50 8.85 3 4 3.93 5.04 6.29 6.71 7.05 7.35 7.60 7.83 4 5 3.64 4.60 5.22 5.67 6.03 6.58 6.80 6.99 5 6 4.90 5.30 5.63 6 6.33 5.90 5.61 3.46 3.34 3.26 4.34 4.16 6.12 5.82 6.32 6.00 6.49 6.16 7 4.68 5.06 7 5.36 5.17 8 4.04 4.53 4.89 5.60 5.77 8 5.40 5.24 4.41 4.76 9 3.20 3.15 3.95 3.88 5.43 5.30 5.02 4.91 4.82 5.59 5.46 5.92 5.74 5.60 5.49 4.33 4.65 5.12 5.03 3.82 4.57 5.20 5.35 3.11 3.08 10 11 12 13 4.26 4.20 4.15 4.51 4.95 3.77 3.73 5.27 4.75 4.69 5.12 5.05 5.39 5.32 4.45 5.19 3.06 3.03 4.88 4.83 3.70 4.11 4.41 4.64 5.13 5.25 14 9 10 11 12 13 14 15 16 17 18 19 20 24 15 3.67 3.65 4.37 4.33 4.59 4.56 3.01 3.00 2.98 2.97 5.08 5.03 4.08 4.05 4.02 4.00 4.99 4.94 4.90 4.86 4.82 4.78 4.74 4.70 4.67 16 17 4.30 4.52 4.99 3.63 3.61 3.59 4.28 4.49 4.96 5.20 5.15 5.11 5.07 5.04 5.01 4.92 18 4.25 4.65 4.79 19 2.96 2.95 2.92 3.98 3.96 4.47 4.44 4.92 4.90 3.58 4.23 4.62 20 4.77 4.68 3.53 3.90 4.17 4.37 4.54 4.81 24

30 30 40 2.89 2.86 2.83 3.49 3.44 3.85 3.79 3.74 4.10 4.04 3.98 4.30 4.23 4.46 4.36 4.31 4.72 4.63 4.82 4.73 40 60 3.40 4.16 4.60 4.52 4.44 4.36 4.29 4.65 60 120 2.80 3.68 4.10 3.36 3.31 120 3.92 3.86 4.55 4.47 4.39 4.24 4.17 4.56 4.47 8 2.77 3.63 4.03 00 D 2 3 4 5 6 7 8 9 10 D2 D