When Performing a Rank Correlation Test, One Alternative to Using $$r _ { S } = \pm \sqrt { \frac { t ^ { 2 } } { t ^ { 2 } + n - 2 } }$$

Multiple Choice

When performing a rank correlation test, one alternative to using the Critical Values of Spearman's Rank Correlation Coefficient table to find critical values is to compute them using this approximation:
$$r _ { S } = \pm \sqrt { \frac { t ^ { 2 } } { t ^ { 2 } + n - 2 } }$$
where $t$ is the $t$ -score from the $t$ Distribution table corresponding to $n - 2$ degrees of freedom. Use this approximation to find critical values of $r _ { \mathrm { S } }$ for the case where $n = 40$ and $\alpha = 0.10$ .

A) $\pm 0.312$
B) $\pm 0.304$
C) $\pm 0.264$
D) $\pm 0.202$