Answered: To test the durability of the material…

Name: To test the durability of the material used for running shoes, a sampl
Uploaded: 2024-03-20T07:07:12.000Z
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Description: To test the durability of the material used for running shoes, a sample is placed in testing device that simulates an average-sized person using the shoes until the material wears out. The material is supposed to last at least an average of 20 months

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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To test the durability of the material used for running shoes, a sample is placed in testing device that simulates an average-sized person using the shoes until the material wears out. The material is supposed to last at least an average of 20 months. Suppose that the wear-out time is characterized by a normal distribution with both μ and σ unknown.

A test on five randomly selected pairs of shoes yields wear-out times of 20, 28, 18, 24, and 25 months.

a) If the mean shoe wear-out time of the sample is is 22 months, or stated differently, what is the power for μ_a = 22?

b) What sample size (n) is needed to achieve β = 0.1 for μ_a = 22 months?

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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