A One-Factor Fixed-Effects ANOVA Is Performed on Data for 5 $\bar{Y}_{.1}-\frac{\bar{Y}_{.2}+\bar{Y}_{.3}}{2}$

Essay

A one-factor fixed-effects ANOVA is performed on data for 5 groups of unequal sizes, and H₀ is rejected at the .05 level of significance. Using the Scheffé procedure, test the contrast that
$\bar{Y}_{.1}-\frac{\bar{Y}_{.2}+\bar{Y}_{.3}}{2}$ at the .05 level of significance given the following information:
df_with = 30, = 5, n₁ = 6, = 7.5, n₂ = 6, = 8.5, n₃ = 6, and MS_with = 9.