Answered: A researcher wants to test whether two…

Name: A researcher wants to test whether two services that purport to increa
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Description: A researcher wants to test whether two services that purport to increase GRE scores differ in their effectiveness. One is Princeton Review (PR), the other is Kaplan (KAP), a variable referred to as GRE-testype. She also decides to look at both the

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 researcher wants to test whether two services that purport to increase GRE scores differ in their effectiveness. One is Princeton Review (PR), the other is Kaplan (KAP), a variable referred to as GRE-testype. She also decides to look at both the verbal (V-GRE) and quantitative (Q-GRE) scores after the training, a variable labeled as Service. She randomly assigns 40 students to each of the programs (total N = 80). The scores below reflect the mean score increases for the students:

	PR	KAP
V-GRE	20.45	31.62
Q-GRE	33.04	22.18

SS_GRE-testtype = 3.76 SS_Service = 3.03 SS _{GRE-testype X Service} = 37.41 SS_WITHIN = 652

Use alpha .05 for all tests and explain the results in terms that could be understood by a lay audience.

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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