Medical Wonders Is a Specialized Interior Design Company Focused on Healing

Medical Wonders is a specialized interior design company focused on healing artwork.The CEO, Kathleen Kelledy claims that artwork has healing effects for patients staying in a hospital, as measured by reduced length of stay.Her current client is a children's cancer hospital.Kathleen is interested in determining the effect of three different pieces of healing artwork on children.She chooses three paintings (a horse photo, a bright abstract, and a muted beach scene) and randomly assigns six hospital rooms to each painting.Analysis of Kathleen's data yielded the following ANOVA table. $$\begin{array} { | l | r | r | r | r | } \hline \text { Source of Variation } & { \text { SS } } & { \text { df } } & { \text { MS } } & { \text { F } } \\\hline \text { Treatment } & 33476.19 & 2 & 16738.1 & 9.457912 \\\hline \text { Error } & 26546.18 & 15 & 1769.745 & \\\hline \text { Total } & 60022.37 & 17 & & \\\hline\end{array}$$ Using $\alpha$ = 0.05, the appropriate decision is _____________.

A) reject the null hypothesis $\mu$ ₁ = $\mu$ ₂= $\mu$ ₃
B) reject the null hypothesis $\mu$ ₁ $\neq$ $\mu$ ₂ $\neq$ $\mu$ ₃
C) do not reject the null hypothesis $\mu$ ₁ $\ge$ $\mu$ ₂ $\ge$ $\mu$ ₃
D) do not reject the null hypothesis $\mu$ ₁ $\le$ $\mu$ ₂ $\le$ $\mu$ ₃
E) inconclusive