Question

Female undergraduates in randomized groups of 30 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 30 18.50 3.41 μ1 x2 30 19.13 3.00 μ2 x3 30 18.47 3.95 μ3 (a) Find a 90% confidence interval for μ1 − μ2. (Round your answers to two decimal places.) lower limit upper limit (b) Find a 90% confidence interval for μ1 − μ3. (Round your answers to two decimal places.) lower limit upper limit (c) Find a 90% 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 90% 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

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