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 α. n = 12, α = 0.01

Answer 1

Answer:

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

And is distributed with n-2 degreed of freedom. df=n-2=12-2=10

The significance level is $\alpha=0.01$ and $\alpha/2 = 0.005$ and for this case we can find the critical values and we got:

$t_{\alpha/2}= \pm 3.169$

Step-by-step explanation:

In order to test the hypothesis if the correlation coefficient it's significant we have the following hypothesis:

Null hypothesis: $\rho =0$

Alternative hypothesis: $\rho \neq 0$

The statistic to check the hypothesis is given by:

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

And is distributed with n-2 degreed of freedom. df=n-2=12-2=10

The significance level is $\alpha=0.01$ and $\alpha/2 = 0.005$ and for this case we can find the critical values and we got:

$t_{\alpha/2}= \pm 3.169$