Answered: Suppose that Kim is a participant in a…

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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Suppose that Kim is a participant in a study that compares several coaching methods to see how they affect math Scholar Aptitude Test (SAT) scores. The grand mean of math SAT scores for all participants (M_y) in the study is 550. The group that Kim participated in had a mean math SAT score of 565. Kim’s individual score on the math SAT was 610.

What was the estimate residual component (of Kim’s score, that is, the part of Kim’s score that was not related to the coaching method? (Both parts of this question call for specific numerical values as answers).

What was that “effect” (a_i) component of Kim's score?

What pattern in grouped data would make SS_within = 0? What pattern within data would make SS_between = 0?

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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