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To determine whether a statistically significant difference exists in work motivation scores between the three groups of employees (Group A, Group B, and Group C), a one-way ANOVA (Analysis of Variance) can be applied. ANOVA is a parametric statistical technique used to compare the means of three or more independent groups. The fundamental assumption of ANOVA is that the populations from which the samples are drawn are normally distributed and have homogeneity of variances. The data for each group is as follows: * Group A: 2, 3, 2, 4, 3, 4, 5, 2, 3, 4 * Group B: 4, 3, 2, 4, 3, 2, 4, 3, 2, 1 * Group C: 3, 2, 3, 4, 2, 3, 5, 4, 2, 3 ### Step 1: State the Hypotheses * Null Hypothesis (H₀): μA = μB = μC (There is no significant difference in work motivation scores among the three groups) * Alternative Hypothesis (H₁): At least one group mean is significantly different ### Step 2: Calculate Group Means and Overall Mean Group A: Sum = 2 + 3 + 2 + 4 + 3 + 4 + 5 + 2 + 3 + 4 = 32 Mean = 32 / 10 = 3.2 Group B: Sum = 4 + 3 + 2 + 4 + 3 + 2 + 4 + 3 + 2 + 1 = 28 Mean = 28 / 10 = 2.8 Group C: Sum = 3 + 2 + 3 + 4 + 2 + 3 + 5 + 4 + 2 + 3 = 31 Mean = 31 / 10 = 3.1 Overall Mean: Total Sum = 32 + 28 + 31 = 91 Total Observations = 10 + 10 + 10 = 30 Overall Mean = 91 / 30 ≈ 3.033 ### Step 3: Calculate Sum of Squares Total Sum of Squares (SST): SST = Σ(X - Grand Mean)² over all observations Group A: (2−3.033)² + (3−3.033)² + (2−3.033)² + (4−3.033)² + (3−3.033)² + (4−3.033)² + (5−3.033)² + (2−3.033)² + (3−3.033)² + (4−3.033)² \= 1.067 + 0.001 + 1.067 ___ _____ ________ ____ __________ ___ ______ ______ _____ ____ ______.
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