Answered: A researcher is interested in examining…

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 examining the effect of emotions on those that are convicted of a crime while under the age of 15. She decides to compare the empathy quotient (EQ) scores of those convicted of violent crimes to those convicted of non-violent crimes. A random sample of 34 violent offenders had a mean score of 33.5 and a standard deviation of 3.5, and another sample of 25 non-violent offenders had a mean of 35 and a standard deviation of 3. Also, suppose that equal variance cannot be assumed. If a higher EQ score indicated increased empathy, construct a 95% confidence interval for the difference in means.

What is the critical value?

What is the lower bound of the confidence interval?

What can she conclude about the difference in empathy between the two groups?

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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