Answered: One of the categories of special…

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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One of the categories of special education are children who are diagnosed with Speech/Language Impairment (SLI). The most common SLI diagnosis is dyslexia. A major difficulty for children with this diagnosis of dyslexia surrounds the skills of reading. A special education teacher is interested in knowing whether a new reading technique increases reading skills for children diagnosed with dyslexia. She uses the WRAT as a way of measuring reading skills and the average for this test is 55 with a standard deviation of 4.5. She takes a random sample of 125 children diagnosed with dyslexia, employs her reading program with them and finds their mean on the WRAT to be 56.1. Test the null hypothesis at the .05 level of significance.

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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