Answered: Suppose the National Transportation…

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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Question

Suppose the National Transportation Safety Board (NTSB) wants to examine the safety of

compact cars, midsize cars, and full-size cars. It collects a sample of three for each of the

treatments (cars types). Using the hypothetical data provided below, test whether the mean

pressure applied to the driver’s head during a crash test is equal for each types of car. Use α = 5%.

	Compact cars	Midsize cars	Full-size cars
	643	469	484
	655	427	456
	702	525	402
Mean	666.67	473.67	447.33
Standard deviation	31.18	49.17	41.68

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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