Answer to Question #267541 in Statistics and Probability for lani

Question

The following table shows the result of correlation analysis between the performance of a student in terms of GPA, and characteristics such as family income, distance of residence from school, size of family, educational attainment of mother and daily allowance of the students.

 

Variables

Correlation coefficient

p value

Family income

0.65

0.0081

Distance of residence from school

0.32

0.0825

Size of family

0.15

0.1019

Educational attainment of mother

0.73

0.0036

Daily allowance

0.56

0.0411

           Legend:           ** significant at (p<0.01)

                                   *significant at (<0.05)

                                   ns not significant

                       

a.      Based on the result of the analyses, which of these variables are significantly correlated? Mark these variable/s using appropriate notation.

b.     Discuss each of the result of the correlation analyses and give its implication.

 

 

 

Answer 1

a.

$H_0:r=0$

$H_a:r\neq 0$

if p-value > $\alpha$ we accept the null hypothesis

so,

significantly correlated for $\alpha=0.01$ and $\alpha=0.05$ :

Family income, p-value = 0.0081

Educational attainment of mother, p-value = 0.0036

significantly correlated for $\alpha=0.05$ :

Daily allowance, p-value = 0.0411

b.

1.The correlation coefficient is significantly DIFFERENT FROM zero at levels 1% and 5%. There IS A SIGNIFICANT LINEAR RELATIONSHIP between the performance of a student and Family income.

2.The correlation coefficient is not significantly DIFFERENT FROM zero at levels 1% and 5%. There IS A not SIGNIFICANT LINEAR RELATIONSHIP between the performance of a student and Distance of residence from school.

3.The correlation coefficient is not significantly DIFFERENT FROM zero at levels 1% and 5%. There IS A not SIGNIFICANT LINEAR RELATIONSHIP between the performance of a student and Size of family.

4.The correlation coefficient is significantly DIFFERENT FROM zero at levels 1% and 5%. There IS A SIGNIFICANT LINEAR RELATIONSHIP between the performance of a student and Educational attainment of mother.

5.The correlation coefficient is not significantly DIFFERENT FROM zero at level 1% . There IS A not SIGNIFICANT LINEAR RELATIONSHIP between the performance of a student and Daily allowance 1%.

The correlation coefficient is significantly DIFFERENT FROM zero at level 5%. There IS A SIGNIFICANT LINEAR RELATIONSHIP between the performance of a student and Daily allowance at level 5%.