Question

A study was conducted to determine whether the final grade of a student in an introductory psychology course is linearly related to his or her performance on the verbal ability test administered before college entrance. The verbal scores and final grades for 10 10 students are shown in the table below. Student 1 2 3 4 5 6 7 8 9 10 Score 75 43 37 53 64 62 43 64 75 55 Grade 81 85 98 71 64 65 84 85 84 68

Answer 1

Correlation test :

To test linear association between verbal scores and final grades of 10 student , we have to perform correlation test..

First we need to find correlation coefficient r for the given data set , we can use excel function =CORREL (x,y) to find the value of r

Therefore correlation coefficient r = -0.3703

H₀ : The significant correlation does not exists between verbal scores and final grades.

H_a : The significant correlation exists between verbal scores and final grades.

Test statistic :

t = =

t = -1.13

Critical value : We are not given  α, so assume  0.05, and we have n = number of pairs of score and grade = 10

degrees of freedom (d.f) = n-2 = 10-2 = 8

Using t distribution table , for  α ( two tail ) =0.05 and d.f = 8

Critical value = 2.306

Critical region: Reject H₀, if | t | ≥ 2.306 Or fail to reject H0 , if | t | < 2.306

|t |is absolute value of t statistic.

Decision : we have t = -1.13 , so | t | = 1.13

As | t | < 2.306, we fail to reject H₀

Conclusion : We do not have significant evidence that correlation exists between verbal scores and final grades.

Or The significant correlation does not exists between verbal scores and final grades.