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.

Large Family Cars	Passenger Vans	Midsize Utility Vehicles
263	148	225
134	240	214
407	338	188
527	695	306
148	547	351
627	475	553
164	321	395

(a) State the null and alternative hypotheses

Test the hypothesis that the mean head injury for each vehicle type is the same at the ?=0.01 level of significance. Use technology to find the? F-test statistic for this data set.

Determine the? P-value and state the appropriate conclusion.

Draw boxplots of the three vehicle types to support the results obtained

Answer 1

The given problem is to test whether the mean head injury resulting from the offset crash is the same for large family​ cars, passenger​ vans, and midsize utility vehicles​ (SUVs). I have used one way ANOVA / F test to test this claim.

HYPOTHESIS:

The hypothesis is given by:

The mean head injury for three different vehicle types are the same.

The mean head injury for at least two different vehicle types differ.

LEVEL OF SIGNIFICANCE:

ONE WAY ANALYSIS OF VARIANCE:

P VALUE:

The P-value for ANOVA / F test is .

CONCLUSION:

Since the p-value is which is greater than , we fail to reject null hypothesis at 1% level and conclude that the mean head injury resulting from the offset crash is the same for three different vehicle types (large family​ cars, passenger​ vans, and midsize utility vehicles)

BOX PLOT:

From the box plot it is evident that there is no significant difference in the mean head injury resulting from the offset crash for three different vehicle types.