Question

A highway safety institution conducts experiments in which cars are crashed into a fixed barrier at 40 mph. In the​ institute's 40-mph offset​ test, 40% of the total width of each vehicle strikes a barrier on the​ driver's side. The​ barrier's deformable face is made of aluminum​ honeycomb, which makes the forces in the test similar to those involved in a frontal offset crash between two vehicles of the same​ weight, each going just less than 40 mph. You are in the market to buy a family car and you want to know if the mean head injury resulting from this offset crash is the same for large family​ cars, passenger​ vans, and midsize utility vehicles​(SUVs). The data in the accompanying table were collected from the​institute's study.

a.) Normal probability plots indicate that the sample data come from normal populations. Are the requirements to use the​ one-way ANOVA procedure​ satisfied?

b.) Test the null hypothesis that the mean head injury for each vehicle type is the same at the α=0.01 level of significance.

c.) What is the P-value

d.) Draw box plots representing the data

Large Family Cars	Passenger Vans	Midsize Utility Vehicles​ (SUVs)
265	149	223
133	239	217
405	340	185
533	698	304
149	554	354
626	470	558
164	324	396

Answer 1

Answer:

a) Yes, all the requirements for use of a one-way ANOVA procedure are satisfied.

b) F0=MS(Tr) /MSE=0.420

c) p value =0.6636

Since p value is 0. 6636(greater than alpha), there is insufficient evidence to reject the null hypothesis. Thus, we cannot conclude that the means are different at alpha=0.01 level of significance

d)