Answered: Polychlorinated biphenyls (PCBs) are a…

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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Polychlorinated biphenyls (PCBs) are a group of synthetic oil-like chemicals that were at
one time widely used as insulation in electrical equipment and were discharged into rivers.
They were discovered to be a health hazard and were banned in the 1970s. Since then, much
effort has gone into monitoring PCB concentrations in waterways. Assume that water
samples are being drawn from a waterway in order to estimate the PCB concentration.
a) Suppose that a random sample of size 80 has a sample mean of 1.69 ppb and a sample
standard deviation of 0.25 ppb. Find a 95% confidence interval for the PCB concentration.
b) Estimate the sample size needed so that a 95% confidence interval will specify the
population mean to within ±0.02 ppb.

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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