Question

r₁, r₁-m₁, (r₁-m₁)², r₂, r₂-m₂, (r₂-m₂)², r₃, r₃-m₃, (r₃-m₃)², r₄, r₄-m₄, (r₄-m₄)²; 3, -2, 4, 5, -1, 1, 8, 0, 0, 8, -1, 1; 3, -2, 4, 3, -3, 9, 5, -3, 9, 9, 0, 0; 4, -1, 1, 5, -1, 1, 8, 0, 0, 7, -2, 4; 6, 1, 1, 7, 1, 1, 9, 1, 1, 10, 1, 1; 6, 1, 1, 8, 2, 4, 8, 0, 0, 10, 1, 1; 8, 3, 9, 8, 2, 4, 10, 2, 4, 10, 1, 1; t₁=30, m₁=5, ss₁=20; t₂=36, m₂=6, ss₂=20; t₃=48, m₃=8, ss₃=14; t₄=54, m₄=9, ss₄=8; x²: 3→9, 3→9, 4→16, 6→36, 6→36, 8→64, 5→25, 3→9, 5→25, 7→49, 8→64, 8→64, 8→64, 5→25, 8→64, 9→81, 8→64, 10→100, 8→64, 9→81, 7→49, 10→100, 10→100, 10→100; σx2=1,298; n=24, gt=168, σx²=1298, k=4, n=6; df_tot=23, df_bet=3, df_with=20; ss_tot=122, ss_bet=60, ss_with=62; ms_bet=20, ms_with=3.1; f=6.45, η²=0.49, tukey hsd=2.65; 1v2: x, 1v3: y, 1v4: y, 2v3: x, 3v4: x, 2v4: y

Explanation:

Answer:

1. \(M_1 = 5\)
2. \(M_2 = 6\)
3. \(M_3 = 8\)
4. \(M_4 = 9\)
5. \(SS_1 = 20\)
6. \(SS_2 = 20\)
7. \(SS_3 = 14\)
8. \(SS_4 = 8\)
9. \(N = 24\)
10. \(GT = 168\)
11. \(\sum X^2 = 1298\)
12. \(k = 4\)
13. \(n = 6\)
14. \(Df_{tot}=23\)
15. \(Df_{bet}=3\)
16. \(Df_{with}=20\)
17. \(SS_{tot}=122\)
18. \(SS_{bet}=60\)
19. \(SS_{with}=62\)
20. \(MS_{bet}=20\)
21. \(MS_{with}=3.1\)
22. \(F = 6.45\)
23. \(\eta^2=0.49\)
24. \(Tukey\ HSD = 2.65\)