Answered: A paper manufacturer has a production…

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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A paper manufacturer has a production process that operates continuously throughout an entire production shift. The paper is expected to have a mean length of 8 inches, and the standard deviation of the length is 0.04 inch. At periodic intervals, a sample is selected to determine whether the mean paper length is still equal to 8 inches or whether something has gone wrong in the production process to change the length of the paper produced. A random sample of 100 sheets is selected, and the mean paper length is 8.003 inches. A 95% confidence interval estimate for the population mean paper length is 7.99516less than or equalsmuless than or equals8.01084. Is it true that you do not know for sure whether the population mean is between 7.99516 and 8.01084 inches?

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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