emale undergraduates in randomized groups of 21 took part in a self-esteem study. The study measured an index of self-esteem from the point of view of competence, social acceptance, and physical attractiveness. Let x1, x2, and x3 be random variables representing the measure of self-esteem through x1 (competence), x2 (social acceptance), and x3 (attractiveness). Higher index values mean a more positive influence on self-esteem. Variable Sample Size Mean x Standard Deviation s Population Mean x1 21 20.32 3.27 μ1 x2 21 19.69 3.77 μ2 x3 21 18.89 3.53 μ3 (a) Find a 99% confidence interval for μ1 − μ2. (Round your answers to two decimal places.) lower limit upper limit (b) Find a 99% confidence interval for μ1 − μ3. (Round your answers to two decimal places.) lower limit upper limit (c) Find a 99% confidence interval for μ2 − μ3. (Round your answers to two decimal places.) lower limit upper limit (d) Comment on the meaning of each of the confidence intervals found in parts (a), (b), and (c). At the 99% confidence level, what can you say about the average differences in influence on self-esteem between competence and social acceptance? between competence and attractiveness? between social acceptance and attractiveness?

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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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emale undergraduates in randomized groups of 21 took part in a self-esteem study. The study measured an index of self-esteem from the point of view of competence, social acceptance, and physical attractiveness. Let x₁, x₂, and x₃ be random variables representing the measure of self-esteem through x₁ (competence), x₂ (social acceptance), and x₃ (attractiveness). Higher index values mean a more positive influence on self-esteem.

Variable	Sample Size	Mean x	Standard Deviation s	Population Mean
x₁	21	20.32	3.27	μ₁
x₂	21	19.69	3.77	μ₂
x₃	21	18.89	3.53	μ₃

(a) Find a 99% confidence interval for μ₁ − μ₂. (Round your answers to two decimal places.)

lower limit
upper limit

(b) Find a 99% confidence interval for μ₁ − μ₃. (Round your answers to two decimal places.)

lower limit
upper limit

lower limit
upper limit

(d) Comment on the meaning of each of the confidence intervals found in parts (a), (b), and (c). At the 99% confidence level, what can you say about the average differences in influence on self-esteem between competence and social acceptance? between competence and attractiveness? between social acceptance and attractiveness?

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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