Answered: Thomas wants to compare the mean…

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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Thomas wants to compare the mean concentration of carbon monoxide (CO) on residential versus commercial streets, since these differ in terms of car traffic. In each of three neighborhoods of Montréal (named A, B, and C below), he randomly chooses four locations for each type of street, for a total of 24 observations (2 street types x 3 neighborhoods x 4 locations). At each location, he measures CO concentration in the air over a period of 10 hours (8:00 AM-6:00 PM), and obtains the following data (in ppm/h). Question: Test whether or not the difference between residential and commercial streets in mean atmospheric CO concentration is the same among the three neighborhoods, and whether or not CO concentration in the air is the same, on average, for the two types of streets. Note that Neighborhood is considered a random block factor in the ANOVA. Use significant level= 0.05.

Neighborhood
A
X,
1.0, 1.2, 0.9, 0.5
(0.9)
1.6, 2.1, 2.5, 2.2
(2.1)
0.4, 0.8, 0.6, 0.2
(0.5)
0.8, 1.4, 1.0, 1.2
(1.1)
1.1, 1.4, 1.5, 1.2
(1.3)
3.0, 2.5, 3.2, 3.7
(3.1)
Residential
0.9
Туре
of
street
Commercial
2.1
X,
1.5
0.8
2.2
X = 1.5
.j.

Thomas has prepared a part of the ANOVA table.
Source of variation
df
SS
MS
Type of street
Neighborhood
Type of street-by-
Neighborhood
2
7.84
3.92
Error
Total
23
19.84

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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