Female undergraduates in randomized groups of 22 took part in a self-esteem study. The study measured...
Female undergraduates in randomized groups of 22 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 | 22 | 20.11 | 2.99 | μ1 |
| x2 | 22 | 18.71 | 3.07 | μ2 |
| x3 | 22 | 17.14 | 3.67 | 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 |
(c) Find a 95% 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 95% 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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