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.
Extracurricular Activity Yes Yes Yes Yes No No No No No No
College Feshamn GPA 3.53 3.38 3.92 3.68 2.97 3.84 3.43 2.81 3.87 2.83
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. 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 Yes Yes Yes Yes No No No No No No
College Feshamn GPA 3.53 3.38 3.92 3.68 2.97 3.84 3.43 2.81 3.87 2.83
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. 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 Yes Yes Yes Yes No No No No No No
College Feshamn GPA 3.53 3.38 3.92 3.68 2.97 3.84 3.43 2.81 3.87 2.83
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.

Explanation / Answer

(A) Here we code the dichotomous variable where extra curricular activity = 1 and no extracurricular activity = 0

Here we will compute the point - biserial correlation coeffcient

Here

rpb = (M1 -M0) sqrt(pq) /sn  

M1 = 3.6275

M0 = 3.2917

p = 0.6, q = 0.4

sp = 0.4041

r = (3.6275 - 3.2917) * sqrt(0.6 * 0.4)/0.4041 = 0.407

(b) Here first we conver r to t where df = 10 - 2 = 8 and alpha = 0.05

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

t = 0.407 * sqrt [8/(1- 0.4072)]

t = 1.26

Here tcritical = 2.306 (Two tailed)

so here t < tcritical so we retain the null hypotheis and conclude that there is no significant relation between variables.

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