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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

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Answer:


t=(r √(n-2))/(√(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

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 \\eq 0

The statistic to check the hypothesis is given by:


t=(r √(n-2))/(√(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

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