Question

For a data set of brain volumes ​(cm3​) and IQ scores of five ​males, the linear correlation coefficient is requals 0.581. Use the table available below to find the critical values of r. Based on a comparison of the linear correlation coefficient r and the critical​ values, what do you conclude about a linear​ correlation? Critical values__.

Number of Pairs of Data n		Critical Value of r
4		0.950
5		0.878
6		0.811
7		0.754
8		0.707
9		0.666
10		0.632
11		0.602
12		0.576

Answer 1

The correlation coefficient would be significant, if the computed correlation coefficient is more than the critical value.

We are given the correlation coefficient here as r = 0.581 which is less than all the critical values except the one for n = 12.

Base on the given data, the correlation coefficient would be significant only if the sample size is greater than or equal to 12.

As we are not given the sample size pairs for which we get the correlation coefficient of 0.581, we can conclude from the given data here that the correlation coefficient is significant only if the sample size is greater than or equal to 12.