Because of potential variability in aging due to different castings and segments on the castings, a Latin square design with / = 7 was used to investigate the effect of heat treatment on aging. With A = castings, B = segments, C = heat treatments, summary statistics include x = 3815.8, Ex; = 297,214.90, Ex.; 2 = 297,200.86, Ex..k = 297,159.02, and EXXjj(k) - = 297,318.65. Obtain the ANOVA table and test at level 0.05 the hypothesis that heat treatment has no effect on aging. (Round your answers to two decimal places.) Source df SS MS f Fo.05 A B C Error Total O State the appropriate hypotheses. O Hoc: 81 # 8 , # ...$ 8, # 0 Hac: all 8 's = 0 O Hoc: 61 = 62 = ... = 67 = 0 Hac: no &k = 0 O Hoc: 81 $ 8 2 # ...$ 8 , # 0 Hac: at least one & = 0 O Hoc: 81 = 62 = ... = 87 =0 Hac: at least one 8* * 0 State the conclusion in the problem context. O Reject Hoc. The data does not suggest that the heat treatment was effective. O Fail to reject Hoc. The data suggests that the heat treatment was effective. O Reject Hoc. The data suggests that the heat treatment was effective. O Fail to reject Hoc. The data does not suggest that the heat treatment was effective