Answered: Students who wish to go to graduate…

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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Students who wish to go to graduate school are often required to take a graduate record exam. It has been suggested that students who prepare using a paper prep book do better, on average, than students who use the online prep materials provided by the exam's administrators. In order to investigate this claim, the mean score, x̅_1, for a random sample of students how use a paper pre book will be compared to the mean score, x̅_2, for a random sample of students who use the online materials. Let the mean score for all students who use paper prep books be μ1μ1 and the mean score for all students who use the online materials be μ2μ2 . Which of the following are appropriate null and alternative hypotheses for this study?

a) Null hypothesis: μ1 = μ2 Alternative hypothesis: μ1 > μ2
b) Null hypothesis: x̅_1 = x̅_2 Alternative hypothesis: x̅_1 > x̅_2

c) Null hypothesis: x̅_1 > x̅_2 Alternative hypothesis: x̅_1 = x̅_2

d) Null hypothesis: x̅_1 = x̅_2 Alternative hypothesis: x̅_1 >= x̅_2

e) Null hypothesis: μ1 > μ2 Alternative hypothesis: μ1 = μ2

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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