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	3.49
Yes	3.31
Yes	3.94
Yes	3.69
No	2.95
No	3.86
No	3.47
No	2.76
No	3.85
No	2.78

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


(b) Using a two-tailed test at a 0.05 level of significance, state the decision to retain or reject the null hypothesis. Hint: You must first convert r to a t-statistic.

Retain the null hypothesis OR Reject the null hypothesis.    

Answer 1

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	Coded activity
Yes	3.49	1
Yes	3.31	1
Yes	3.94	1
Yes	3.69	1
No	2.95	0
No	3.86	0
No	3.47	0
No	2.76	0
No	3.85	0
No	2.78	0

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

M1=3.6075

M2=3.2783

s=0.4480

p=4/10=0.4

q=6/10=0.6

r = (3.6075-3.2783)*sqrt(0.4*0.6)/0.4480

=0.360

(b) Using a two-tailed test at a 0.05 level of significance, state the decision to retain or reject the null hypothesis. Hint: You must first convert r to a t-statistic.

t=1.0914

DF = n-2 =8

Table value of t with 8 DF at 0.05 level =2.306

Calculated t =1.0914 < 2.306 , the table value

The null hypothesis is not rejected.

Retain the null hypothesis