In a study among college students, participants (ages 18-28 years old) completed a self-report questionnaire about their self-esteem. What statistical analysis would you use to see if there was a relationship between the two variables listed? Group of answer choices: t-test ANOVA Regression Correlation
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Female undergraduates in randomized groups of 15 took part in a self-esteem study ("There's More to Self-Esteem than Whether It Is High or Low: The Importance of Stability of Self-Esteem," by M. H. Kernis et al., Journal of Personality and Social Psychology, Vol. 65, No. 6 ). The study measured an index of self-esteem from the points of view of competence, social acceptance, and physical attractiveness. Let $x_{1}, x_{2},$ and $x_{3}$ be random variables representing the measure of self-esteem through $x_{1}$ (competence), $x_{2}$ (social acceptance), and $x_{3}$ (attractiveness). Higher index values mean a more positive influence on self-esteem. $$\begin{array}{ccccc} \hline & & & \text { Standard } & \text { Population } \\ \text { Variable } & \text { Sample Size } & \text { Mean } \bar{x} & \text { Deviation } s & \text { Mean } \\ \hline x_{1} & 15 & 19.84 & 3.07 & \mu_{1} \\ x_{2} & 15 & 19.32 & 3.62 & \mu_{2} \\ x_{3} & 15 & 17.88 & 3.74 & \mu_{3} \\ \hline \end{array}$$ (a) Find an $85 \%$ confidence interval for $\mu_{1}-\mu_{2}$ (b) Find an $85 \%$ confidence interval for $\mu_{1}-\mu_{3}$ (c) Find an $85 \%$ confidence interval for $\mu_{2}-\mu_{3}$ (d) Comment on the meaning of each of the confidence intervals found in parts (a), (b), and (c). At the $85 \%$ 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?
Estimation
Estimating $\mu_{1}-\mu_{2}$ and $p_{1}-p_{2}$
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