Answered: A sample of N= 50 individuals is…

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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A sample of N= 50 individuals is selected from a population with a mean of 50. A treatment is administered to the individuals in the sample and, after treatment, the sample has a mean of X=51 and SS=27, 220. (a) Compute a 95% confidence interval for u, the population mean for the treatment group. (b) Compute Cohen's d to estimate the size of the described effect. (c) Perform a hypothesis test to decide whether the population mean of the treatment group is significantly larger than the mean of the general population. (d) Compute and interpret a Bayes factor for the model (either He or H,) with the best predictive adequacy. (e) Compute and interpret the posterior model probability for the winning model chosen in part (d).

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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