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
Your answer is correct.
(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.
Your answer is correct.
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
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