Question

Suppose that a sample of 13 pairs of data produced a test statistic of r = 0.562. A significance level of a = 0.01 is to be used. (a) Find the critical values that would be used to test for significant linear correlation. Do not type "" in front of your answer the + is already given in front of the answer box below). Round your answer to 3 places after the decimal point, if necessary. er r= + (b) Is there significant linear correlation in this case? There is not significant linear correlation. There is significant linear correlation. Submit Question

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Answer 1

a) The sample size is n = 13, so then the number of degrees of freedom is

df = n−2 =13−2 = 11

The corresponding critical correlation value r_c for a significance level of α=0.01, for a two-tailed test is:

r_c = $\pm 0.684$

b) r = 0.562

Observe that in this case, the null hypothesis is rejected if ∣r∣> r_c​ = 0.684.

Here r = 0.562 < 0.684 so we accept H₀.

Conclusion - There is not significant linear correlation.

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