Answered: A study of parental empathy for…

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 study of parental empathy for sensitivity cues and baby temperament (higher scores mean more empathy) was performed. Let x₁ be a random variable that represents the score of a mother on an empathy test (as regards her baby). Let x₂ be the empathy score of a father. A random sample of 37 mothers gave a sample mean of x₁ = 68.70. Another random sample of 34 fathers gave x₂ = 59.72. Assume that σ₁ = 11.69 and σ₂ = 11.59.

(a)

Let μ₁ be the population mean of x₁ and let μ₂ be the population mean of x₂. Find a 99% confidence interval for μ₁ – μ₂. (Round your answers to two decimal places.)

lower limitupper limit

(b)

Examine the confidence interval and explain what it means in the context of this problem. Does the confidence interval contain all positive, all negative, or both positive and negative numbers? What does this tell you about the relationship between average empathy scores for mothers compared with those for fathers at the 99% confidence level?

Because the interval contains only positive numbers, we can say that the mothers have a higher mean empathy score.Because the interval contains both positive and negative numbers, we can not say that the mothers have a higher mean empathy score. We can not make any conclusions using this confidence interval.Because the interval contains only negative numbers, we can say that the fathers have a higher mean empathy score.

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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