Using State Data (N = 50) for the Year 2000 $n = 50$

question 125

Essay

Using state data (n = 50) for the year 2000, a statistics student calculated a matrix of correlation coefficients for selected variables describing state averages on the two main scholastic aptitude tests (ACT and SAT). (a) In the spaces provided, write the two-tailed critical values of the correlation coefficient for α = .05 and α = .01 respectively. Show how you derived these critical values. (b) Mark with * all correlations that are significant at α = .05, and mark with ** those that are significant at α = .01. (c) Why might you expect a negative correlation between ACT% and SAT%? (d) Why might you expect a positive correlation between SATQ and SATV? Explain your reasoning. (e) Why is the matrix empty above the diagonal?
Correlation Matrix ( $n = 50$ states $)$

$\begin{array}{|c|c|c|c|c|}\text { ACT } & A C T \% & \text { SAT\% } & \text { SATQ } & \text { SATV }\\\hline\text { ACT } & 1.000 & & & & \\\hline A C T \% &-0.232 & 1.000 & & & \\\hline \text { SAT\% } &0.139 & -0.966 & 1.000 & & \\\hline \text { SATQ } & 0.213 & 0.818 & -0.856 & 1.000 & \\\hline \text { SATV }&0.092 & 0.862 & -0.889 & 0.963 & 1.000 \\\hline\end{array}$


$A C T =$ average composite $A C T$ score
$A C T \%$ = percent of high school grads taking the ACT
SAT\% = percent of high school graduates taking SAT test
$S A T Q$ = average SAT quantitative test score
SATV = average SAT verbal test score
Critical value for $.05$
Critical value for $.01$

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Definitions:

Compassionate Personality

A character trait characterized by a desire to help those in need and a deep empathy for others' suffering.

Attribution Theory

A psychological concept that explains how individuals attribute causes and effects to behaviors or events, examining the cognitive process behind these explanations.

Dispositional Attribution

The tendency to attribute someone's behavior to their personality or character rather than to situational factors.

Situational Attribution

The process of attributing a person's behavior to external circumstances or situational factors rather than to internal traits or motivations.