30. Listed below are head injury data from crash test dummies. These measurements are in hic, which denotes a standard head injury criterion. The TI-84 Plus display presents the results of a one-way ANOVA to determine whether different car categories have the same mean.Head Injury in a Car Crash (hic)Small Cars290406371544374501376499479475Medium Cars245502474505393264368510296349Large Cars342216335698216169608432510332(a) Is the design balanced? Why or why not?(b) ConstructanANOVAtable.(c) Can you conclude that the different car categories have the same mean? Use the 0.05 level of significance. (you do not need to show all the steps of the hypothesis test, but explain your decision.)

From the given Information, a) The design is balanced, since all the possible level combinations…

Answered: 30. Listed below are head injury data…

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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30. Listed below are head injury data from crash test dummies. These measurements are in hic, which denotes a standard head injury criterion. The TI-84 Plus display presents the results of a one-way ANOVA to determine whether different car categories have the same mean.

Head Injury in a Car Crash (hic)
Small Cars	290	406	371	544	374	501	376	499	479	475
Medium Cars	245	502	474	505	393	264	368	510	296	349
Large Cars	342	216	335	698	216	169	608	432	510	332

(a) Is the design balanced? Why or why not?

(b) ConstructanANOVAtable.

(c) Can you conclude that the different car categories have the same mean? Use the 0.05 level of significance. (you do not need to show all the steps of the hypothesis test, but explain your decision.)

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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