Answered: Eric is interested in how sleep…

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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Eric is interested in how sleep deprivation effects performance on a learning task. Eric takes a sample of 10k (10, 000) rats subjects them to a learning task, he then keeps them up for a full 24 hours to ensure that they are sleep deprived. At this point he has them do the learning task again. He now wants to calculate the 95% confidence interval around the mean difference, which of the following formulas should he use:

m_D±1.96(s_mD)

m±1.96(σ_m)

m₁-m₂±1.96(s_m1-m2)

m₁-m₂±1.645(s_m1-m2)

m_D±1.645(s_mD)

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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