Female undergraduates in randomized groups of 17 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 17 20.25 3.34 ?1 x2 17 20.46 3.84 ?2 x3 17 17.00 3.25 ?3 (a) Find a 99% confidence interval for ?1 - ?2. (Use 2 decimal places.) lower limit ? upper limit ? (b) Find a 99% confidence interval for ?1 - ?3. (Use 2 decimal places.) lower limit ? upper limit ? (c) Find a 99% confidence interval for ?2 - ?3. (Use 2 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?