Answered: Suppose that we need to compute 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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Suppose that we need to compute the probability of Type II error and the power for the following hypothesis test: H_o: μ = 5 and H₁: μ > 5 with the following decision rule: reject H_o if [-5]/[0.1/] > 1.645 or 5 + 1.645*[0.1/] = 5.041, when we know that the true population mean is given by μ = 5.15. Then the solution should proceed as follows: Since μ = 5.15, β = P(≤xc| μ = μ*) = P(≤5.041| μ*=5.15) = P([5.15 - 5.041]//[0.1/] = P(z≤1.05) and the power of the test is given by power = 1 – .0111 = .899. Is it true or false? Note that xc is thecritical value from the appropriate sampling distribution of the sample mean, μ is the population mean under null hypothesis, μ * is the true population mean, and x-bar is the sample mean.

True

False

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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