(Optional, advanced problem) Using the Fisher transformation (described in footnote 5), carry out a two-tailed test of the hypothesis that the population correlation coefficient for the situation of given problem is p = 0.22. Use α = 0.05.
Problem
A study was conducted to determine whether a correlation exists between consumers' perceptions of a television commercial (measured on a special scale) and their interest in purchasing the product (measured on a scale). The results are n = 65 and r = 0.37. Is there statistical evidence of a linear correlation between the two variables?