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Description: It was randomly chosen as a sample of 18 units from a stack known to have a normal distribution. It was observed that the mean of this sample was 62 and the variance was 16. In line with the findings obtained, test whether the average of the stack fr

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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It was randomly chosen as a sample of 18 units from a stack known to have a normal distribution. It was observed that the mean of this sample was 62 and the variance was 16. In line with the findings obtained, test whether the average of the stack from which this sample was drawn is different than 57 at a significance level of 1%, and interpret the decision you made as a result of the test. While testing the hypothesis test, apply the 4 stages and show them separately.

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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