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 I: x1; n1 = 15 855 1550 1230 875 1080 2330 1850 1860 2340 1080 910 1130 1450 1260 1010 Region II: x2; n2 = 14 540 810 790 1230 1770 960 1650 860 890 640 1180 1160 1050 1020 (a) Use a calculator with mean and standard deviation keys to verify that x1, s1, x2, and s2. (Round your answers to one decimal place.) x1 = ppm s1 = ppm x2 = ppm s2 = ppm (b) Let μ1 be the population mean for x1 and let μ2 be the population mean for x2. Find a 99% confidence interval for μ1 − μ2. (Round your answers to one decimal place.) lower limit ppm upper limit ppm (c) Explain what the confidence interval means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 99% level of confidence, is one region more interesting than the other from a geochemical perspective? Because the interval contains both positive and negative numbers, we can not say that one region is more interesting than the other.Because the interval contains only positive numbers, we can say that region I is more interesting than region II. Because the interval contains only negative numbers, we can say that region II is more interesting than region I.We can not make any conclusions using this confidence interval. (d) Which distribution (standard normal or Student's t) did you use? Why? Standard normal was used because σ1 and σ2 are known.Student's t was used because σ1 and σ2 are unknown. Standard normal was used because σ1 and σ2 are unknown.Student's t was used because σ1 and σ2 are known.

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 I: x1; n1 = 15 855 1550 1230 875 1080 2330 1850 1860 2340 1080 910 1130 1450 1260 1010 Region II: x2; n2 = 14 540 810 790 1230 1770 960 1650 860 890 640 1180 1160 1050 1020 (a) Use a calculator with mean and standard deviation keys to verify that x1, s1, x2, and s2. (Round your answers to one decimal place.) x1 = ppm s1 = ppm x2 = ppm s2 = ppm (b) Let μ1 be the population mean for x1 and let μ2 be the population mean for x2. Find a 99% confidence interval for μ1 − μ2. (Round your answers to one decimal place.) lower limit ppm upper limit ppm (c) Explain what the confidence interval means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 99% level of confidence, is one region more interesting than the other from a geochemical perspective? Because the interval contains both positive and negative numbers, we can not say that one region is more interesting than the other.Because the interval contains only positive numbers, we can say that region I is more interesting than region II. Because the interval contains only negative numbers, we can say that region II is more interesting than region I.We can not make any conclusions using this confidence interval. (d) Which distribution (standard normal or Student's t) did you use? Why? Standard normal was used because σ1 and σ2 are known.Student's t was used because σ1 and σ2 are unknown. Standard normal was used because σ1 and σ2 are unknown.Student's t was used because σ1 and σ2 are known.

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Description: 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 phosph

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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Region I: x₁; n₁ = 15
855	1550	1230	875	1080	2330	1850	1860
2340	1080	910	1130	1450	1260	1010
Region II: x₂; n₂ = 14
540	810	790	1230	1770	960	1650	860
890	640	1180	1160	1050	1020

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

x₁	= ppm
s₁	= ppm
x₂	= ppm
s₂	= ppm

(b) Let μ₁ be the population mean for x₁ and let μ₂ be the population mean for x₂. Find a 99% confidence interval for μ₁ − μ₂. (Round your answers to one decimal place.)

lower limit	ppm
upper limit	ppm

(c) Explain what the confidence interval means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 99% level of confidence, is one region more interesting than the other from a geochemical perspective?

Because the interval contains both positive and negative numbers, we can not say that one region is more interesting than the other.Because the interval contains only positive numbers, we can say that region I is more interesting than region II. Because the interval contains only negative numbers, we can say that region II is more interesting than region I.We can not make any conclusions using this confidence interval.

(d) Which distribution (standard normal or Student's t) did you use? Why?

Standard normal was used because σ₁ and σ₂ are known.Student's t was used because σ₁ and σ₂ are unknown. Standard normal was used because σ₁ and σ₂ are unknown.Student's t was used because σ₁ and σ₂ are known.

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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