Answered: Suppose we want to estimate 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 we want to estimate the concentration (μg/mL)

of a specific dose of ampicillin in the urine after various pe-
riods of time. We recruit 25 volunteers who have received

ampicillin and find they have a mean concentration of 7.0
μg/mL with a standard deviation of 2.0 μg/mL. Assume
the underlying population distribution of concentrations is
normally distributed.
Problem a) Find a 95% CI for the population mean concentration.
Problem b) Find a 99% CI for the population variance of the
concentrations.
Problem c) How large a sample would be needed to ensure
that the length of the CI in Problem a is 0.5 μg/mL
assuming the sample standard deviation remains at
2.0 μg/mL?

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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