Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of r given the number of pairs of data n and the significance level $\alpha$
n=14, $\alpha = 0.01$
A) r=0.661
B) r=0.684
C) $r = \pm 0.532$
D) $r = \pm 0.661$

Question

Suppose you will perform a test to determine whether there is sufficient evidence to support a claim of a linear correlation between two variables. Find the critical values of  r  given the number of pairs of data  n  and the significance level $\alpha$
 n=14, $\alpha = 0.01$
A)  r=0.661 
B)  r=0.684 
C) $r = \pm 0.532$
D) $r = \pm 0.661$

Quizplus · Accepted Answer

To find the critical values of $r$ for a given number of pairs $n$ and a significance level $\alpha$, one typically uses a table of critical values for the Pearson correlation coefficient. For $n = 14$ and $\alpha = 0.01$ (two-tailed), the critical value is approximately $\pm 0.661$. This means that if the computed correlation coefficient is greater than $0.661$ or less than $-0.661$, there is sufficient evidence to reject the null hypothesis of no linear correlation at the 0.01 significance level.

Suppose You Will Perform a Test to Determine Whether There α\alphaα

Suppose You Will Perform a Test to Determine Whether There $\alpha$