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

Question

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

Quizplus · Accepted Answer

Since the p-value is less than the significance level of 0.05, we reject the null hypothesis and conclude that at least one of the three paintings has a different effect on children's length of stay in the hospital. No further information is given to make post-hoc comparisons between the three paintings.

Medical Wonders Is a Specialized Interior Design Company Focused on Healing