Answered: In order to estimate the mean…

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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In order to estimate the mean debt-to-equity ratio of its loan portfolio, the bank randomly selects 12 of its commercial loan accounts. Audits of these twelve companies found the following 12 debt-to-equity ratios.

1.04	1.08	1.13	1.18	1.23	1.32
1.41	1.46	1.55	1.57	1.70	1.77

Note: the sample standard deviation of these 12 ratios is s = 0.245

If you crunch all the numbers in the previous part, the 98% confidence interval for the mean ratio of the bank’s entire portfolio is calculated to be 1.37±0.191.37±0.19

According to the above confidence interval, can the bank conclude with 98% confidence that the mean ratio of its entire portfolio of commercial loans does NOT exceed 1.5? ["", ""] and Why? ["", "", "", ""]

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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