Question: Chinese students from public schools in Hong Kong were the subjects of a study designed to investigate the relationship between various measures of parental behavior and other variables. The data were obtained using questionnaires and an assessment administered to 720 students. Using items from the questionnaire, three continuous variables were constructed, parental control (an indication of the amount of control that the parents exercised over the behavior of their child), self-esteem (of the students) and reading achievement (a scaled measure that has items on the reading achievement assessment as components). Increasing scores on each of these variables indicated higher levels of the construct being measured.

a. (2 points) The sample correlation between parental control and self-esteem was found to be r= -0.47. Is this correlation significant? (In everyday language, when someone asks whether a correlation is significant, they are usually implying that they would like to know the results of a test for the statistical significance of this correlation; this is synonymous with testing the null hypothesis that the population correlation is 0. Note that determining whether a “correlation is significant” in this context is not the same as quantifying a measure of the importance of the correlation coefficient magnitude using an effect size measure). In your answer, provide the appropriate hypotheses, test statistic and p-value and state whether you would say the correlation is significant (use a = 0.05 ).

b. (3 points) Compute an appropriate measure of the practical importance of the sample correlation coefficient and provide a short substantive summary of your results from part 1 a along with this measure.

c. (5 points) The sample was divided into two groups, males and females, and the correlation between parental control and reading achievement was found to be r = -0.37 for males (n = 360) and r = -0.26 for females (n = 360). Test whether the gender difference in the correlation between parental control and reading achievement is statistically significant. (use a = 0.05 )