A researcher measures the relationship between Internet use (hours per week) and

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.

(a) Compute the Pearson correlation coefficient. (Round your answer to three decimal places.)
1

(b) Compute the coefficient of determination. (Round your answer to three decimal places.)
2

(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.    

Internet Use Social Interaction X Y 7 3 8 5 5 7 7 7 13 5 5 8 4 2 5 6 2 10 12 3

Explanation / Answer

a) The correlation coeff

from Excel

The correlation between x and y is -0.4724

hence there is negative correlation between x and y

b) coefficient of determination is

R2 =(-0.4724)2=0.2231

c) Test for correlation

H0: There is no relation between x and y

H1: There is a relation betyween x and y

alpha:5%

Test statistic:

where n=10 and r=-0.4724

t= -1.5160

t critical value at 8 df=2.31

Conclusion: t cal < t critical value, we do not reject the H0. Hence claim is not significant

Internet Use Social Interaction Internet Use 1 Social Interaction -0.47239 1

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