Question

gender	gpa	final	total
gender	Pearson Correlation	1	.208*	-.140	-.143
	Sig. (2-tailed)		.033	.156	.145
	N	105	105	105	105
gpa	Pearson Correlation	.208*	1	.223*	.199*
	Sig. (2-tailed)	.033		.022	.041
	N	105	105	105	105
final	Pearson Correlation	-.140	.223*	1	.881**
	Sig. (2-tailed)	.156	.022		.000
	N	105	105	105	105
total	Pearson Correlation	-.143	.199*	.881**	1
	Sig. (2-tailed)	.145	.041	.000
	N	105	105	105	105

Report the lowest magnitude correlation in the intercorrelation matrix, including degrees of freedom, correlation coefficient, p value, and effect size. Interpret the effect size. Specify whether or not to reject the null hypothesis for this correlation.

Answer 1

the lowest magnitude of correlation in the given intercorrelation matrix happens between the variables "gender" and "final" with a correlation value - 0.140.

Degree of freedom=N-2=105-2=103.

P-valuie= 0.156.

Effect size= The correlation value -0.140 is fall within the interval of effect size -0.1 to -0.3

Interpretation of effect size: The effect size of the estimated correlation value is in the range -0.1 to -0.3. Hence, the these variables have a small strength of association.

Specify whether or not to reject the null hypothesis for this correlation.

Ans: The P-value is 0.156 and greater than 0.05 level of significance. Hence, we fail to reject the null hypothesis and conclude that there is no significant association between these two variables at the 0.05 level of significance.