Medical Wonders Is a Specialized Interior Design Company Focused on Healing

Multiple Choice

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.
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