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

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 :

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

The t-statistics is given by:

Degree of freedom is given by:

df = n - 2 = 12 - 2 = 10

The significance level for this test is

Now, the critical value r is given by:

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

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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:

The degrees of freedom of the test is:

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

The critical values of r are:

*Use the r critical value table.

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

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