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. Complete parts​ (a) through​ (c) below.

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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. Complete parts​ (a) through​ (c) below.

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.
Complete parts (a) through (d) below.
Click the icon to view the data table.
.....
(a) State the null and alternative hypotheses.
A. Ho: HCars = HVans = HsUVs and H,: at least one mean is different
B. Ho: HCars = HVans = HsUVs and H,: all means are different
O C. Ho: HCars = Hvans = HsuVs and H1: HCars <HVans < HsuVs
(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 largest sample standard deviation is more than twice the smallest sample standard deviation.
C. No, because the samples are not independent.
D. No, because the populations are not normally distributed.
(c) Test the hypothesis that the mean head injury for each vehicle type is the same at the a = 0.01 level of significance.
Use technology to find the F-test statistic for this data set.
(Round to three decimal places as needed.)
Determine the P-value and state the appropriate conclusion below.
Since the P-value is
there is
evidence to reject the null hypothesis. Thus, we
conclude that the means are different at the a = 0.01 level of significance.
can
(Round to four decimal places as needed.)
Transcribed Image Text: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. Complete parts (a) through (d) below. Click the icon to view the data table. ..... (a) State the null and alternative hypotheses. A. Ho: HCars = HVans = HsUVs and H,: at least one mean is different B. Ho: HCars = HVans = HsUVs and H,: all means are different O C. Ho: HCars = Hvans = HsuVs and H1: HCars <HVans < HsuVs (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 largest sample standard deviation is more than twice the smallest sample standard deviation. C. No, because the samples are not independent. D. No, because the populations are not normally distributed. (c) Test the hypothesis that the mean head injury for each vehicle type is the same at the a = 0.01 level of significance. Use technology to find the F-test statistic for this data set. (Round to three decimal places as needed.) Determine the P-value and state the appropriate conclusion below. Since the P-value is there is evidence to reject the null hypothesis. Thus, we conclude that the means are different at the a = 0.01 level of significance. can (Round to four decimal places as needed.)
Head Injuries
Large Family Cars Passenger Vans Midsize Utility Vehicles (SUVS)
267
148
226
134
238
218
410
339
185
529
696
304
ar
149
546
353
624
475
546
165
323
399
Print
Done
Transcribed Image Text:Head Injuries Large Family Cars Passenger Vans Midsize Utility Vehicles (SUVS) 267 148 226 134 238 218 410 339 185 529 696 304 ar 149 546 353 624 475 546 165 323 399 Print Done
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