Female undergraduates in randomized groups of 15 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 Mean Standard Deviation Population Size Mean 15 19.48 2.92 X1 X2 X3 (a) Find a 90% confidence interval for µ1 – H2. (Round your answers to two decimal places.) lower limit 15 19.90 3.98 H2 15 17.42 3.60 upper limit (b) Find a 90% confidence interval for µ1 - H3. (Round your answers to two decimal places.) lower limit upper limit (c) Find a 90% confidence interval for µ2 - 43. (Round your answers to two decimal places.) lower limit upper limit

Question
Female undergraduates in randomized groups of
15 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
Mean Standard Deviation Population
Size
Mean
15
19.48 2.92
X1
X2
X3
(a) Find a 90% confidence interval for µ1 – H2.
(Round your answers to two decimal places.)
lower limit
15
19.90 3.98
H2
15
17.42 3.60
upper limit
(b) Find a 90% confidence interval for µ1 - H3.
(Round your answers to two decimal places.)
lower limit
upper limit
(c) Find a 90% confidence interval for µ2 - 43.
(Round your answers to two decimal places.)
lower limit
upper limit
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Transcribed Image Text

Female undergraduates in randomized groups of 15 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 Mean Standard Deviation Population Size Mean 15 19.48 2.92 X1 X2 X3 (a) Find a 90% confidence interval for µ1 – H2. (Round your answers to two decimal places.) lower limit 15 19.90 3.98 H2 15 17.42 3.60 upper limit (b) Find a 90% confidence interval for µ1 - H3. (Round your answers to two decimal places.) lower limit upper limit (c) Find a 90% confidence interval for µ2 - 43. (Round your answers to two decimal places.) lower limit upper limit

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