Female undergraduates in randomized groups of 12 took part in a self-esteem stud
ID: 3055166 • Letter: F
Question
Female undergraduates in randomized groups of 12 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 xStandard Deviation sPopulation Mean 19.55 20.39 17.49 3.20 3.77 3.53 X2 12 12 (a) Find a 99% confidence interval for,11- lower limit upper limit 2: (Round your answers to two decimal places.) Enter a number 3- (Round your answers to two decimal places.) (b) Find a 99% confidence interval for,11- lower limit upper limit (c) Find a 99% confidence interval for 2- lower limit upper limit 3- (Round your answers to two decimal places.) (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?Explanation / Answer
a)
Test and CI for Two Variances
Two-Sample T-Test and CI
Sample N Mean StDev SE Mean
1 12 19.6 20.4 5.9
2 12 3.20 3.77 1.1
Difference = ? (1) - ? (2)
Estimate for difference: 16.35
99% CI for difference: (-0.52, 33.22)
T-Test of difference = 0 (vs ?): T-Value = 2.73 P-Value = 0.012 DF = 22
Both use Pooled StDev = 14.6623
The 99% confidence interval is ? (-0.52, 33.22)
b)
Two-Sample T-Test and CI
Sample N Mean StDev SE Mean
1 12 20.4 17.5 5.0
2 12 3.77 3.53 1.0
Difference = ? (1) - ? (2)
Estimate for difference: 16.62
99% CI for difference: (2.10, 31.14)
T-Test of difference = 0 (vs ?): T-Value = 3.23 P-Value = 0.004 DF = 22
Both use Pooled StDev = 12.6167
c)
Two-Sample T-Test and CI
Sample N Mean StDev SE Mean
1 12 19.6 17.5 5.0
2 12 3.20 3.53 1.0
Difference = ? (1) - ? (2)
Estimate for difference: 16.35
99% CI for difference: (1.83, 30.87)
T-Test of difference = 0 (vs ?): T-Value = 3.17 P-Value = 0.004 DF = 22
Both use Pooled StDev = 12.6167
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