A researcher is interested in the relationship between the time (measured in minutes) spent exercising per week and scores on a life satisfaction scale that ranges from 10 to 70, with higher scores signifying more satisfaction. She collects data from 25 s and computes a Pearson correlation coefficient, and finds r = .53.
a. State a null and a directional alternative hypothesis for her study.
b. What is the df for this study?
c. Can the researcher reject the null hypothesis at the p < .05 if she uses a two-tailed test? (Use Table 7.4 to first determine the critical r value that the obtained r must exceed.) Explain your answer.
d. Can the researcher reject the null hypothesis at the p < .01 if she uses a two-tailed test? (Use Table 7.4 to determine the critical r value for this example.) Explain your answer.