A study was conducted to compare the effect of three diet types on the milk yield of cows (in lbs). The sample size, the sample mean, and sample variance for each method are given below.

Diet A: n ₁  = 9, X ₁  = 39.1, s ²  ₁  = 24.6
Diet B: n ₂  = 8, X ₂  = 29.9, s ²  ₂  = 16.4
Diet C: n ₃  = 10, X ₃  = 45.9, s ²  ₁  = 10.3

(a) Construct an ANOVA table including all relevant sums of squares, mean squares, and degrees of freedom.

(b) Perform an overall F test to determine whether the population means of milk yield are the same or not among the three diet types.