Answered: Researchers studied the effect of…

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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Researchers studied the effect of road-junction design on travel efficiency. They created two four-way inter- sections (i.e., a crossroads). One intersection was a typical four-way stop: cars had to stop and wait for the way to be clear before they could drive through the intersection. The other intersection used a roundabout: cars only had to stop if another car was already in the roundabout. They timed how long it took for cars to pass though the intersection in moderately heavy traffic conditions. A sample of 8 cars were monitored at the four-way-stop intersection. Here are their times (in seconds): 9, 13, 14, 14, 15, 11, 11, 14. A sample of 9 cars were monitored at the roundabout intersection. Here are their times (in seconds): 10, 3, 12, 15, 9, 15, 9, 9, 8. Calculate the mean time (and standard deviation) taken by the cars in each intersection and analyze the data to determine if the means are significantly different. Calculate the effect size, Cohen's d. Report your findings as a sentence or two that could be in the Results section of an APA-style research article.

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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