Question

Linear Correlation Coefficient In Exercises 9–12, the linear correlation coefficient r is provided. Use Table 2-11 on page 71 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?

Using the data from Exercise 5 “Brain Volume and IQ,” the linear correlation coefficient is r = 0.127.

Short answer

The computed value of correlation coefficient is 0.127, and it lies within the critical values -0.878 and 0.878.

Thus, it can be concluded that there is no correlation between brain volume and IQ scores.

Step-by-step solution

Given information

The value of the correlation coefficient between the variables, brain volume and IQ score of males, is r = 0.127.

Refer to Exercise 5; the number of paired observations is 5, which is n.

Significance test for correlation 

To identify whether the given linear correlation coefficient is significant or not, the computed value of ris compared to the critical values of r.

The criteria to make the decision include the following:

• If the computed value lies between the critical values, it can be concluded that there is no significant linear correlationbetween the two variables.
• If the computed value does not lie between the critical values, it can be concluded that there is a significant linear correlation between the two variables.

Make the conclusion  

The value of r between brain volume and IQ scores is equal to 0.127.

The number of data pairs = 5

The critical value of r is observed from Table 2-11, corresponding to the number of paired data in the sample. The critical values are obtained as -0.878 and 0.878.

Since the given value of r lies within the interval of -0.878 and +0.878, it can be said that there is no linear correlation between brain volume and IQ scores.