Answered: researcher is interested in determining…

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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Question

A researcher is interested in determining if her controversial class on altering study-habits will actually alter the SAT scores of students who are studying for the SAT. She is not stating specifically that her class will make the students scores better or worse, just altered (i.e., a two-tailed test). The average SAT score for the population of students who take the SAT is 500. The standard deviation for this population is 100. This population is normally distributed. The mean SAT score for a random sample of 40 students from the study-habits class is 550.

State the hypotheses involved.
Calculate the Z score.
Based on a cut-off point or alpha level of .01 (1%), what decision would you make about your hypotheses? Explain this decision.
Make conclusions regarding the specifics of this study.
Calculate Cohen’s d and discuss the magnitude of the effect size.

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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