Answered: A magazine claims that the brand 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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Question

A magazine claims that the brand of shoe you buy can have a major impact on how fast you run. A researcher decides to test this assertion and gathers a group of seven (N=7) runners and asks each of them to run a mile wearing each of the four different types of shoes (Nike, Adidas, Asics, and Brooks) and records how quickly the runners complete their miles wearing each type of shoe. Conduct a within subjects (AKA repeated measures) ANOVA, at alpha = 0.05, to see if the runners mile times are significantly different depending on the type of shoe they wear.

Identify the correct alternative hypothesis

A. At least two mean mile times are different from at least two other mean mile times between the four different types of shoes being tested
B. There is a significant difference in mean mile time between the four different types of shoes being tested
C. At least one mean mile time is different from at least two other mean mile times between the four different types of shoes being tested
D. At least one mean mile time is different from at least one other mean mile time between the four different types of shoes being tested

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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