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Name: A two-sided hypothesis test is being conducted for testing the mean of
Uploaded: 2024-03-20T07:07:12.000Z
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Description: A two-sided hypothesis test is being conducted for testing the mean of a normal distribution at the 90% level. The hypothesized mean value is 60 whereas the true mean is 61 with the variance being equal for both the hypothesized and real distribution

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 two-sided hypothesis test is being conducted for testing the mean of a normal distribution at the 90% level. The hypothesized mean value is 60 whereas the true mean is 61 with the variance being equal for both the hypothesized and real distributions at the value of 12.20. The sample size is 9. What are the values of the following in the asked order: Pr(Failing to reject the null hypothesis when it is false), Pr(Rejecting the null hypothesis when it is true), the power of the hypothesis test?

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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