Answered: During the production of boiler plate,…

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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During the production of boiler plate, test pieces are subjected to a load, and their
elongations are measured. In one particular experiment, five tests will be made, at loads (in
MPa) of 11, 37, 54, 70, and 93. The least-squares line will be computed to predict
elongation from load. Confidence intervals for the mean elongation will be computed for
several different loads. Which of the following intervals will be the widest? Which will be
the narrowest?
a) The 95% confidence interval for the mean elongation under a load of 53 MPa.
b) The 95% confidence interval for the mean elongation under a load of 72 MPa.
c) The 95% confidence interval for the mean elongation under a load of 35 MPa.

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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