Female undergraduates in randomized groups of 15 took part in a self-esteem study (“There’s More to Self-Esteem than Whether It Is High or Low: The Importance of Stability of Self-Esteem,” by M. H. Kernis et al., Journal of Personality and Social Psychology, Vol. 65, No. 6). The study measured an index of self-esteem from the points 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.

(a) Find an 85% con­fidence interval for m₁ – m₂.

(b) Find an 85% con­fidence interval for m₁ – m₃.

(c) Find an 85% confi­dence interval for m₂ – m₃.

(d) Interpretation Comment on the meaning of each of the con­fidence intervals found in parts (a), (b), and (c). At the 85% 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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Population Mean Standard Vaibl Sample Size MeanDeviation s 15 15 15 19.84 19.32 17.88 3.07 3.62 3.74 Xi x3