Question

Suppose you will perform a test to determine whether there is sufficient evidence to support a

Answer 1

Answer:

The critical values of r are -0.708 and 0.708.

Step-by-step explanation:

A statistical test is being performed to determine whether there is any linear correlation between two variables.

The hypothesis can be defined as follows:

H₀: There is no  linear correlation between two variables, i.e. ρ = 0.

Hₐ: There is a significant linear correlation between two variables, i.e. ρ ≠ 0.

The test statistic is given as follows:

$t = \frac{r\sqrt{n-2}}{\sqrt{1-r^{2}}}$

The degrees of freedom of the test is:

$\text{df}=n-2=12-2=10$

The significance level of the test is, α = 0.01.

The critical values of r are:

$r_{\alpha/2, (n-2)}=r_{0.01/2, (12-2)}=r_{0.005, 10}=\pm0.708$

*Use the r critical value table.

Thus, the critical values of r are -0.708 and 0.708.