Answered: The article “Dynamics of Insulin Action…

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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The article “Dynamics of Insulin Action in Hypertension: Assessment from Minimal Model
Interpretation of Intravenous Glucose Tolerance Test Data” (R. Burattini, M. Morettini, et
al., Med Biol Eng Comput, 2011:831–841) compared levels of an insulin sensitivity index SI
in patients with high blood pressure and patients with normal blood pressure. Ten patients
with high blood pressure had a mean value of 3.4 with a standard deviation of 0.6, and eight
patients with normal blood pressure had a mean value of 7.9 with a standard deviation of
0.6. Units are 10⁻⁵ · min⁻¹ · pmol⁻¹. Find a 98% confidence interval for the difference in
mean levels between those with high blood pressure and those with normal blood pressure.

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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