To test whether extracurricular activity is a good predictor of college success,
ID: 3040142 • Letter: T
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 3.48 Yes 3.29 Yes 3.91 Yes 3.73 No 2.97 No 3.79 No 3.41 No 2.73 No 3.92 No 2.79 (a) Code the dichotomous variable and then compute a point-biserial correlation coefficient. (Round your answer to three decimal places.)
Explanation / Answer
Result:
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 3.48 Yes 3.29 Yes 3.91 Yes 3.73 No 2.97 No 3.79 No 3.41 No 2.73 No 3.92 No 2.79 (a) Code the dichotomous variable and then compute a point-biserial correlation coefficient. (Round your answer to three decimal places.)
Data coded as yes =1 and no = 0
Extracurricular Activity
GPA
Yes
1
3.48
Yes
1
3.29
Yes
1
3.91
Yes
1
3.73
No
0
2.97
No
0
3.79
No
0
3.41
No
0
2.73
No
0
3.92
No
0
2.79
point-biserial correlation r = (M1-M0)*sqrt(pq)/s
M1 = mean (for the entire test) of the group that received the positive binary variable (i.e. the “1”).
M0 = mean (for the entire test) of the group that received the negative binary variable (i.e. the “0”).
Sn = standard deviation for the entire test.
p = Proportion of cases in the “1” group.
q = Proportion of cases in the “0” group.
M1= 3.6025 , M2= 3.2683
s=0.4492
p=0.4, q=0.6
r = (3.6025-3.2683)*sqrt(0.4*0.6)/0.4492
=0.364479
=0.364 ( three decimals).
Extracurricular Activity
GPA
Yes
1
3.48
Yes
1
3.29
Yes
1
3.91
Yes
1
3.73
No
0
2.97
No
0
3.79
No
0
3.41
No
0
2.73
No
0
3.92
No
0
2.79
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