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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

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.5: Comparing Sets Of Data

Problem 13PPS

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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?

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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