Question

To test whether extracurricular activity is a good predictor of college success, a college administrator records whether students participated in extracurricular activities during high school and their subsequent college freshman GPA.

Extracurricular Activity	College Freshman GPA
Yes	3.57
Yes	3.34
Yes	3.90
Yes	3.67
No	3.00
No	3.88
No	3.45
No	2.80
No	3.90
No	2.82

A) Code the dichotomous variable and then compute a point-biserial correlation coefficient. (Round your answer to three decimal places.)

_____

Answer 1

Answer:

Given that,

To test whether the extracurricular activity is a good predictor of college success, a college administrator records whether students participated in extracurricular activities during high school and their subsequent college freshman GPA.

Extracurricular Activity	College Freshman GPA
Yes	3.57
Yes	3.34
Yes	3.90
Yes	3.67
No	3.00
No	3.88
No	3.45
No	2.80
No	3.90
No	2.82

(A).

Code the dichotomous variable and then compute a point-biserial correlation coefficient:

First converting Yes to 1 and No to 0 we get,

	x	y
	1	3.57	0.6	0.137	0.36	0.0188	0.0822
	1	3.34	0.6	-0.093	0.36	0.0087	-0.0558
	1	3.90	0.6	0.467	0.36	0.2181	0.2802
	1	3.67	0.6	0.237	0.36	0.0562	0.1422
	0	3.00	-0.4	-0.433	0.16	0.1875	0.1732
	0	3.88	-0.4	0.477	0.16	0.1998	-0.1908
	0	3.45	-0.4	0.017	0.16	0.0003	-0.0068
	0	2.80	-0.4	-0.633	0.16	0.4007	0.2532
	0	3.90	-0.4	0.467	0.16	0.2181	-0.1868
	0	2.82	-0.4	-0.613	0.16	0.3758	0.2452
Total	4	34.33			2.4	1.684	0.736
Mean	0.4	3.433			SS_{x}	SS_{y}	SS_{xy}

The correlation coefficient (r)

=0.736/ 2.0104

=0.366096299

r= 0.366 (Approximately)

** Please do the comment for any doubt or clarification.