A psychiatrist is concerned about his daughter, who has suffered from extremely low self esteem and high anxiety since entering high school last year. Wondering if many of his daughter’s peers have the same troubles, he collects a random ample of high school girls and anonymously how much they agree or disagree (on a scale from 1 to 7, with 1 being “strongly disagree” and 7 being “strongly agree”) with the following statements: (X) “I felt better about myself before I started high school” and (Y) “I have felt very anxious since I started high school.” Compute a Pearson’s correlation coefficient for the following data and indicate whether the correlation is significant.
X Y
7…………… 5
6…………… 4
4…………… 3
5…………… 6
3…………… 2
6…………… 7
5…………… 5