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Name: The strength limit of a specific type of a cable is random variable wi
Uploaded: 2024-03-20T07:07:12.000Z
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Description: The strength limit of a specific type of a cable is random variable with mean value of 1500 kg and standard deviation 175 kg. The factory that manufactures this type of cables claims that they improved the materials that they used and the new resista

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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The strength limit of a specific type of a cable is random variable with mean value of 1500 kg and standard deviation 175 kg. The factory that manufactures this type of cables claims that they improved the materials that they used and the new resistance limit of the cable has increased. We randomly chose a sample of 50 cables and the mean strength limit was 1570 kg. If the strength limit in the specific type of cable is normally distributed with a significance level of 0.05, can we state that the claim of the manufacture factory is true? Justify your answer.

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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