Final answer:
The value of r needed to achieve significance at the .05 level with 30 pairs of scores can be determined by referring to a table of critical values for the correlation coefficient using the degrees of freedom, which is n - 2 (28 in this case).
Step-by-step explanation:
The question asks for the value of the correlation coefficient r that is needed to achieve significance at alpha = .05 with 30 pairs of scores. To determine significance, we utilize the degrees of freedom, which in correlation tests is given by n - 2. So, with 30 pairs of scores, the degrees of freedom (df) would be 28. Consulting a table of critical values for the correlation coefficient at the .05 significance level with df = 28, we find the critical value.
If the sample correlation r is greater than this critical value or its negative counterpart (for a two-tailed test), then it is considered significant, meaning the null hypothesis can be rejected, and it is concluded that there is a significant linear relationship between the two variables in question.