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 questions below. LOADING... Click the icon to view the data table. Large_Family_Cars Passenger_Vans Midsize_Utility_Vehicles 266 148 226 133 239 216 406 341 185 532 693 310 149 548 349 629 470 547 167 321 394 (a) State the null and alternative hypotheses. A. H0: μCars=μVans=μSUVs and H1: all means are different B. H0: μCars=μVans=μSUVs and H1: μCars<μVans<μSUVs C. 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. No, because the samples are not independent. B. No, because the largest sample standard deviation is more than twice the smallest sample standard deviation. C. No, because the populations are not normally distributed. D. Yes, all the requirements for use of a one-way ANOVA procedure are satisfied. (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. F0=nothing (Round to three decimal places as needed.) Determine the P-value and state the appropriate conclusion below. Since the P-value is nothing, there is ▼ insufficientinsufficient sufficientsufficient evidence to reject the null hypothesis. Thus, we ▼ cancan cannotcannot conclude that the means are different at the α=0.01 level of significance. (Round to four decimal places as needed.)

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 questions below. LOADING... Click the icon to view the data table. Large_Family_Cars Passenger_Vans Midsize_Utility_Vehicles 266 148 226 133 239 216 406 341 185 532 693 310 149 548 349 629 470 547 167 321 394 (a) State the null and alternative hypotheses. A. H0: μCars=μVans=μSUVs and H1: all means are different B. H0: μCars=μVans=μSUVs and H1: μCars<μVans<μSUVs C. 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. No, because the samples are not independent. B. No, because the largest sample standard deviation is more than twice the smallest sample standard deviation. C. No, because the populations are not normally distributed. D. Yes, all the requirements for use of a one-way ANOVA procedure are satisfied. (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. F0=nothing (Round to three decimal places as needed.) Determine the P-value and state the appropriate conclusion below. Since the P-value is nothing, there is ▼ insufficientinsufficient sufficientsufficient evidence to reject the null hypothesis. Thus, we ▼ cancan cannotcannot conclude that the means are different at the α=0.01 level of significance. (Round to four decimal places as needed.)

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Related questions

Concept explainers

Question

below.

Click the icon to view the data table.
Large_Family_Cars Passenger_Vans Midsize_Utility_Vehicles
266 148 226
133 239 216
406 341 185
532 693 310
149 548 349
629 470 547
167 321 394

(a) State the null and alternative hypotheses.

H0: μCars=μVans=μSUVs

and H1: all means are different

H0: μCars=μVans=μSUVs

and H1: μCars<μVans<μSUVs

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?

No, because the samples are not independent.

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

No, because the populations are not normally distributed.

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

α=0.01

level of significance.

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

F0=nothing

(Round to three decimal places as needed.)

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

Since the P-value is

nothing,

there is

▼

insufficientinsufficient

sufficientsufficient

evidence to reject the null hypothesis. Thus, we

▼

cancan

cannotcannot

conclude that the means are different at the

α=0.01

level of significance.

(Round to four decimal places as needed.)

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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