12th Edition

ISBN: 9780321836960

Author: Mario F. Triola

Publisher: PEARSON

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Textbook Question

Chapter 12.2, Problem 1BSC

In Exercises 1-4, use the following listed chest deceleration measurements (in g, where g is the force of gravity) from samples of small, midsize, and large cars. (These values are from Data Set 13 in Appendix B.)Also shown (on the next page) are the SPSS results for analysis of variance. Assume that we plan to use a 0.05 significance level to test the claim that the different size categories have the same mean chest deceleration in the standard crash test.

Chest Deceleration Measurements (g) from a Standard Crash Test

Small	44	39	37	54	39	44	42
Midsize	36	53	43	42	52	49	41
Large	32	45	41	38	37	38	33

SPSS

	Sum of Squares	d	Mean Square	F	Ski
Between Groups	200.857	2	100.429	3 283	.06
Within Group	049.714	18	30.540
Total	750.571	20

1. ANOVA

a. What characteristic of the data above indicates that we should use one-way analysis of variance?
b. If the objective is to test the claim that the three size categories have the same mean chest deceleration, why is the method referred to as analysis of variance?

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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Chapter 11, Problem 1FDD

Chapter 12.2, Problem 2BSC

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Chapter 12 Solutions

Elementary Statistics

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Solution Summary: The author explains that the characteristic of the data indicates the use of one-way analysis of variance.

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