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Name: Aimed at finding substantial earnings decreases, a random sample of 23
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Description: Aimed at finding substantial earnings decreases, a random sample of 23 firms with substantial earnings decreases showed that the mean return on assets 3 years previously was 0.058 and the sample standard deviation was 0.055. An independent random sam

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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Aimed at finding substantial earnings decreases, a random sample of 23 firms with substantial earnings decreases showed that the mean return on assets 3 years previously was 0.058 and the sample standard deviation was 0.055. An independent random sample of 23 firms without substantial earnings decreases showed a mean return of 0.146 and a standard deviation 0.058 for the same period. Assume that the two population distributions are normal with equal standard deviations. Test, at the 5% level, the null hypothesis that the population mean returns on assets are the same against the alternative that the true mean is higher for firms without substantial earnings decreases.

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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