15. 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, writ- ing, and speech were assessed using a number of tests whose results were summarized by a profi- ciency 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 assump- tions? Explain. Proficiency score for Gray-matter second density language (mm³/voxel) 0.26 0.44 0.89 1.26 1.69 1.97 1.98 2.24 2.24 2.58 2.50 -0.070 -0.080 -0.008 -0.009 -0.023 -0.009 -0.036 -0.029 -0.008 -0.023 -0.006 Proficiency score for Gray-matter second density language (mm³/voxel) 2.75 3.25 3.85 3.04 2.55 2.50 3.11 3.18 3.52 3.59 3.40 -0.008 -0.006 0.022 0.018 0.023 0.022 0.036 0.059 0.062 0.049 0.033

15. 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, writ- ing, and speech were assessed using a number of tests whose results were summarized by a profi- ciency 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 assump- tions? Explain. Proficiency score for Gray-matter second density language (mm³/voxel) 0.26 0.44 0.89 1.26 1.69 1.97 1.98 2.24 2.24 2.58 2.50 -0.070 -0.080 -0.008 -0.009 -0.023 -0.009 -0.036 -0.029 -0.008 -0.023 -0.006 Proficiency score for Gray-matter second density language (mm³/voxel) 2.75 3.25 3.85 3.04 2.55 2.50 3.11 3.18 3.52 3.59 3.40 -0.008 -0.006 0.022 0.018 0.023 0.022 0.036 0.059 0.062 0.049 0.033

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.3: Measures Of Spread

Problem 1GP

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