Female undergraduates in randomized groups of 20 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.VariableSample SizeMean xStandard Deviation sPopulation Meanx12018.923.13μ1x22020.463.14μ2x32017.074.09μ3(a) Find a 95% confidence interval for μ1 − μ2. (Round your answers to two decimal places.)lower limit upper limit (b) Find a 95% confidence interval for μ1 − μ3. (Round your answers to two decimal places.)lower limit upper limit (c) Find a 95% confidence interval for μ2 − μ3. (Round your answers to two decimal places.)lower limit upper limit

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MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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Female undergraduates in randomized groups of 20 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	20	18.92	3.13	μ₁
x₂	20	20.46	3.14	μ₂
x₃	20	17.07	4.09	μ₃

(a) Find a 95% confidence interval for μ₁ − μ₂. (Round your answers to two decimal places.)

lower limit
upper limit

(b) Find a 95% confidence interval for μ₁ − μ₃. (Round your answers to two decimal places.)

lower limit
upper limit

lower limit
upper limit

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