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 College Freshman GPA 3.55 Yes Yes Yes 3.36 3.93 Yes 3.65 NO NO 3.85 NO 3.45 No 2.75 No NO 2.80 (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 to a statistic Retain the null hypothesis Reject the null hypothesis. You may need to use the appropriate table in Appendix C to answer this question.

Answer 1

S.No х Y 1 1 1 1 2 3 4 5 6 7 8 9 10 Total 1 2 2 3.55 3.36 3.93 3.65 2.94 3.85 3.45 2.75 3.92 2.8 34.2 (x-x)' 0.3600 0.3600 0.3600 0.3600 0.1600 0.1600 0.1600 0.1600 0.1600 0.1600 2.4000 SSX (y-7) 0.02 0.00 0.26 0.05 0.23 0.18 0.00 0.45 0.25 0.38 1.8330 (x-x)(y-7) -0.0780 0.0360 -0.3060 -0.1380 -0.1920 0.1720 0.0120 -0.2680 0.2000 -0.2480 -0.8100 2 2 2 2 16 1.600 Mean 3.4200 SSY SXY

p(number of 1's)=	4
q(number of 1's)=	6
Mx(1) =	3.6225
My(2) =	3.285
Point biserial r =(Mx-My)*sqrt(pq/(nSSy)=	0.386

b)

retain the null hypothesis