Answered: Speed of light In 1882 Michelson…

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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Speed of light In 1882 Michelson measured the speed of
light (usually denoted c as in Einstein’s famous equation
E = mc2
). His values are in km/sec and have 299,000

subtracted from them. He reported the results of 23 tri-
als with a mean of 756.22 and a standard deviation of

107.12.
a) Find a 95% confidence interval for the true speed of
light from these statistics.
b) State in words what this interval means. Keep in mind
that the speed of light is a physical constant that, as
far as we know, has a value that is true throughout the
universe.
c) What assumptions must you make in order to use your
method?

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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