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 a.
n=12. a.= 0.01​

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.

Answer 2

From the 'r' table, the values of 'r' are -0.708 and 0.708.and this can be determined by using the hypothesis test.

Given :

• Suppose you will perform a test to determine whether there is sufficient evidence to support the claim of a linear correlation between two variables.
• Number of pairs of data n and the significance level a is n = 12, a = 0.01​.

The hypothesis test is performed in this problem. The null and alternate hypothesis is:

$\rm H_0 : p=0$

$\rm H_1:p\neq 0$

The t-statistics is given by:

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

Degree of freedom is given by:

df = n - 2 = 12 - 2 = 10

The significance level for this test is $\alpha = 0.01$

Now, the critical value r is given by:

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

So, from the 'r' table, the values of 'r' are -0.708 and 0.708.

For more information, refer to the link given below:

https://brainly.com/question/2817633