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 $\alpha$ $$n = 12 , \alpha = 0.01$$
A) $r = 0.735$
B) $r = \pm 0.576$
C) $r = \pm 0.708$
D) $r = 0.708$

Question

Quizplus · Accepted Answer

To find the critical value of r, we need to use the following formula:
$$r_{crit} = \pm \frac{t_{\alpha/2}}{\sqrt{n-2+t_{\alpha/2}^2}}$$
where t is the critical value of the t-distribution with n-2 degrees of freedom and significance level of $\alpha/2$ (since it's a two-tailed test). We can find the value of t using a t-table. For $\alpha = 0.01$ and 10 degrees of freedom (n-2), we get $t_{0.005} = 3.169$.

Plugging in the values, we get:
$$r_{crit} = \pm \frac{3.169}{\sqrt{12-2+3.169^2}}$$
Simplifying, 
$$r_{crit} = \pm 0.7078$$
Therefore, the best choice is C, as it is the closest option to the calculated critical value.

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

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