Answered: The Glen Valley Steel Company…

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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C2(c): The Glen Valley Steel Company manufactures steel bars. If the production process is working properly, the process is normally distributed with a mean length of 2.8m. Bars longer than 2.8m can be used by cutting them to 2.8m. However, bars shorter than 2.8m have to be scrapped. A random sample of 25 bars yield a mean length of 2.73m with a sample standard deviation of 0.20m. The process is adjusted if there is sufficient evidence the mean length of the bars is less than 2.8m. The production manager would like to determine whether the process should be adiusted using an appropriate hypothesis test at a 5% significance level.

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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