To test whether extracurricular activity is a good predictor of college success,

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. (a) Code the dichotomous variable and then compute a point-biserial correlation coefficient. (b) Using a two-tailed test at a 0.05 level of significance, state the decision to retain or reject the null hypothesis. Retain the null hypothesis. Reject the null hypothesis.

Explanation / Answer

(a) Assume Extra curricular activity Yes = 1 and No = 0

Here point biserial correlation coefficient rpb = (M1 -M0)/sn sqrt [n1 n0 /n2 ]

M1 = 3.62 ; M2 = 3.29 ; sn = 0.43

n1 = 4; n0 = 6 and n = 10

rpb = (3.62 - 3.29)/ 0.43 * sqrt [4 * 6/10 * 10]

= 0.7674 * 0.4899

= 0.376

now r = 0.376

so t = r sqrt [ (n-2)/ (1-r2 )]

t = 0.376 * sqrt [(10-2)/ (1 -0.3762 )]

t = 0.376 * sqrt [8/ 0.8586]

t = 1.1477

so critical values of t for alpha = 0.05 and dF = 8 are tcr = 2.306

so here t < tcr so we can not reject the null hypohtesis.

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