Answered: Inorganic phosphorous is a naturally…

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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Inorganic phosphorous is a naturally occurring element in all plants and animals, with concentrations increasing progressively up the food chain (fruit < vegetables < cereals < nuts < corpse). Geochemical surveys take soil samples to determine phosphorous content (in ppm, parts per million). A high phosphorous content may or may not indicate an ancient burial site, food storage site, or even a garbage dump. Independent random samples from two regions gave the following phosphorous measurements (in ppm). Assume the distribution of phosphorous is mound-shaped and symmetric for these two regions.

Region 1: x_1;n₁=15

857	1,551	1,230	875	1,080	2,330	1,850	1,860
2,340	1,080	910	1,130	1,450	1,260	1,010

region 11: x₂;n₂-14

538	812	790	1,230	1,770	960	1,650	860
890	640	1,180	1,160	1,050	1,020

(a)Use a calculator with mean and standard deviation keys to verify that x₁, s₁, x₂, and s₂. (Round your answers to four decimal places.)

x₁= ppm

s₁= ppm

x₂= ppm

s₂= ppm

(b)Let ?₁ be the population mean for x₁ and let ?₂ be the population mean for x₂. Find an 80% confidence interval for ?₁ − ?₂. (Round your answers to one decimal place.)

lower limit =_ppm

upper limit =__ppm

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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