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

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 $.01$