Does learning a second language change brain structure? Mechelli et al. (2004) tested 22 native Italian speakers who had learned English as a second language. Proficiencies in reading, writing, and speech were assessed using a number of tests whose results were summarized by a proficiency score. Gray-matter density was measured in the left inferior parietal region of the brain using a neuroimaging technique, as mm³ of gray matter per voxel. (A voxel is a picture element, or “pixel,” in three dimensions.) The data are listed in the accompanying table.

a. Display the association between the two variables in a scatter plot.

b. Calculate the correlation between second language proficiency and gray-matter density.

c. Test the null hypothesis of zero correlation.

d. What are your assumptions in part (c)?

e. Does the scatter plot support these assumptions? Explain.

f. Do the results demonstrate that second language proficiency affects gray-matter density in the brain? Why or why not?