Answered: 2006 2016 0.010 0.120 ….…

Name: Once a month samples of sea level from Key West, FL in 2016 had a mean
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Description: Once a month samples of sea level from Key West, FL in 2016 had a mean level of 0.113m and standard deviation of 0.0492m. Ten years earlier, once a month samples of sea level in the same location had mean of 0.014m and standard deviation 0.0373m. Res

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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Once a month samples of sea level from Key West, FL in 2016 had a mean level of 0.113m and standard deviation of 0.0492m. Ten years earlier, once a month samples of sea level in the same location had mean of 0.014m and standard deviation 0.0373m. Researchers wish to estimate the change in mean sea level in Key West from 2006 to 2016 with 95% confidence.

Year

Jan Feb …. Dec

Mean SD

2006

2016

0.010 0.120 …. 0.104

0.010 0.101 …. 0.082

0.133 0.0492

0.014 0.0373

Diff

0.000 0.019 …. 0.022

0.099 0.0380

a. Explain why this is considered paired data.

b. What is the point estimate for the average difference?

c. What is the standard error of the difference in means?

d. What is the margin of error?

e. Construct and interpret the confidence interval for the mean difference in sea level between 2006 and 2016.

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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