Question

# A highway safety institution conducts experiments in which cars are crashed into a fixed barrier at...

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.

Large_Family_Cars   Passenger_Vans   Midsize_Utility_Vehicles
267   148   224
134   238   218
409   338   184
527   691   306
150   555   354
622   471   552
167   323   394

​(a) State the null and alternative hypotheses.

A.

H0: μCars=μVans=μSUVs and H1: at least one mean is different

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

A.

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

B.

​No, because the samples are not independent.

C.

​No, because the populations are not normally distributed.

D.

​No, because the largest sample standard deviation is more than twice the smallest sample standard deviation.

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

Use technology to find the​ F-test statistic for this data set.

F0equals=__?__

​(Round to three decimal places as​ needed.)

The statistical software output for this problem is:

Hence,

F = 0.413

#### Earn Coins

Coins can be redeemed for fabulous gifts.