Answered: The circumference of a species of tree…

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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2. The circumference of a species of tree was thought to be different depending on geographical factors. An SRS of 60 trees of this species is selected in Sequoyah National Forest, where it is found that ?1̅ = 6 m with a standard deviation ?1 = 3 m. A second SRS of size 40 trees of the same species is independently selected inYellowstone National Forest, and it is found that ?̅2 = 4 m with a standard deviation ?2 = 2 m. A 95% confidence interval for the difference of means was computed to be (1.01, 2.99). Explain what one can conclude from this confidence interval. In particular, can one believe there is a difference in mean circumference between Sequoyah and Yellowstone?

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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