Answered: In a study, we see that plastic…

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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Question 8

Plastic Microfiber Pollution on Shorelines

In a study, we see that plastic microparticles are contaminating the world’s shorelines and that much of the pollution appears to come from fibers from washing polyester clothes. The same study also took samples from ocean beaches. Five samples were taken from each of 18 different shorelines worldwide, for a total of 90 samples of size 250 mL. The mean number of plastic microparticles found per 250 mL of sediment was 18.3 with a standard deviation of 8.2.

(a) Find a 95% confidence interval for the mean number of polyester microfibers per 250 mL of beach sediment.

Round your answers to two decimal places.

The 95% confidence interval is to .

(b) What is the margin of error?

Round your answer to two decimal places.

margin of error =

the absolute tolerance is +/-0.05

(c) If we want a margin of error of only ±0.5 with 95% confidence, what sample size is needed?

Round your answer up to the nearest integer.

sample size =

the absolute tolerance is +/-3

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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