Answered: In a sample of 100 steel wires the…

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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In a sample of 100 steel wires the average breaking strength is 50KN, with a standard
deviation of 2KN.
a. Find a 95% confidence interval for the mean breaking strength of this type of wire.
b. Find a 99% confidence interval for the mean breaking strength of this type of wire.
c. An engineer claims that the mean breaking strength is between 49.7KN and 50.3KN. With
what level of confidence can this statement be made?
d. How many wires must be sampled so that a 95% confidence interval specifies the mean
breaking strength to within ± 0.30KN?
e. How many wires must be sampled so that a 99% confidence interval specifies the mean
breaking strength to within ± 0.30KN?

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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