Region I: x1; n1 = 12 540 810 790 790 340 800 890 860 820 640 970 720 Region II: x2; n2 = 16 750 870 700 810 965 350 895 850 635 955 710 890 520 650 280 993 (a) Use a calculator with mean and standard deviation keys to calculate x1, s1, x2, and s2. (Round your answers to four decimal places.) 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 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. Because the interval contains both positive and negative numbers, we can not say that one region is more interesting than the other.We can not make any conclusions using this confidence interval.

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. The Hill of Tara is a very important archaeological site in Ireland. It is by legend the seat of Ireland's ancient high kings†. Independent random samples from two regions in Tara gave the following phosphorous measurements (ppm). Assume the population distributions of phosphorous are mound-shaped and symmetric for these two regions.

Region I: x₁; n₁ = 12
540	810	790	790	340	800
890	860	820	640	970	720

Region II: x₂; n₂ = 16
750	870	700	810	965	350	895	850
635	955	710	890	520	650	280	993

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

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

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

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

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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