Question

A researcher measures the relationship between Internet use (hours per week) and social interaction (hours per week) in a sample of 10 students. The following table lists the hypothetical results of this study.

Internet Use	Social Interaction
X	Y
5	5
9	6
4	8
7	7
11	6
3	7
2	3
6	5
1	10
11	4

(a) Compute the Pearson correlation coefficient. (Round your answer to three decimal places.)


(b) Compute the coefficient of determination. (Round your answer to three decimal places.)


(c) 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.

Answer 1

a) Pearson correlation coefficient (r) :

So correlation coefficient ( r ) is ,

b)

Coefficient of determination = R² = r^2 = (-0.352)^2 = 0.124

c)

Hypothesis :

Critical value for Person correlation coefficient :

Using Person correlation coefficient table :

Let , = 0.05 , n = 10

Critical value for Person correlation coefficient = r_c = 0.632

Reject if the absolute value of r is greater than table value r_c

It is observed that | r | = 0.352 < r_c = 0.632

So , Fail to reject null hypothesis.

Conclusion : There is no relationship between Internet use (hours per week) and social interaction