Data for head injury measurements (in HIC, which is a standard head injury criterion) from samples of small, midsize, and large cars involved in the standard crash test were used to produce the accompanying ANOVA table. Using a 0.05 significance level, test the claim that the different size categories have the same mean head injury measurement. Does the size of a car appear to affect head injuries? ANOVA tableDialog content starts Sum ofSquaresdfMean SquareFSig.Between Groups73630.272236815.1361.6060.227Within Groups435546.4431922923.497 Total509176.71521 What are the hypotheses to test?H0:H1:The test statistic is(Round to two decimal places as needed.) The P-value is(Round to three decimal places as needed.) ___________H0. Since the P-value is__________than the significance level, there___________sufficient evidence to refute the claim that the different size categories have the same mean head injury measurement. It__________that the size of a car affects head injuries.

We have to interpret the result of ANOVA.

Answered: Data for head injury measurements (in…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Data for head injury measurements (in HIC, which is a standard head injury criterion) from samples of small, midsize, and large cars involved in the standard crash test were used to produce the accompanying ANOVA table. Using a 0.05 significance level, test the claim that the different size categories have the same mean head injury measurement. Does the size of a car appear to affect head injuries?

ANOVA table

Dialog content starts

	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	73630.272	2	36815.136	1.606	0.227
Within Groups	435546.443	19	22923.497
Total	509176.715	21

What are the hypotheses to test?

H0:

H1:

The test statistic is

(Round to two decimal places as needed.)

The P-value is

(Round to three decimal places as needed.)

___________H0. Since the P-value is__________than the significance level, there

___________sufficient evidence to refute the claim that the different size categories have the same mean head injury measurement. It__________that the size of a car affects head injuries.

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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