To find the critical value for the linear correlation coefficient \( r \) at a significance level of \( \alpha = 0.01 \) with a sample size of \( n = 20 \), we first need to calculate the degrees of freedom, which is given by:
\[ df = n - 2 = 20 - 2 = 18 \]
Next, we can look up the critical value of \( r \) for a significance level of \( 0.01 \) and \( df = 18 \) in a table of critical values for the correlation coefficient or using a statistical software.
For \( df = 18 \) and \( \alpha = 0.01 \) (two-tailed), the critical value is typically around \( 0.575 \).
So, the correct answer is:
A) 0.575