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	3.32
Yes	3.93
Yes	3.70
No	2.97
No	3.87
No	3.46
No	2.77
No	3.83
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.Reject the null hypothesis.    

Answer 1

changing Yes to 1 and No to 0 ;

S.No	X	Y	(x-x̅)2	(y-y̅)2	(x-x̅)(y-y̅)
1	1	3.48	0.3600	0.0048	0.0414
2	1	3.32	0.3600	0.0083	-0.0546
3	1	3.93	0.3600	0.2694	0.3114
4	1	3.7	0.3600	0.0835	0.1734
5	0	2.97	0.1600	0.1945	0.1764
6	0	3.87	0.1600	0.2107	-0.1836
7	0	3.46	0.1600	0.0024	-0.0196
8	0	2.77	0.1600	0.4109	0.2564
9	0	3.83	0.1600	0.1756	-0.1676
10	0	2.78	0.1600	0.3982	0.2524
Total	4	34.11	2.4000	1.7581	0.7860
Mean	0.400	3.411	SSX	SSY	SXY

a)

correlation coefficient r=

Sxy/(√Sxx*Syy) =

0.383

b)

test stat t=	r*(√(n-2)/(1-r2))=	1.171
P value    =		0.2751

since test statistic is smaller than critical value 2.306

Retain the null hypothesis