Question

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	19.34	2.57	μ1
x2	20	20.39	3.77	μ2
x3	20	17.35	3.46	μ3

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

upper limit:

lower limit:

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

upper limit:

lower limit:

(c) Find a 99% confidence interval for μ₂ − μ₃. (Round your answers to two decimal places.)

upper limit:

lower 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?

Answer 1