[See Steps] A psychiatrist is concerned about his daughter, who has suffered from extremely low self-esteem and high anxiety since entering high school
Question: 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 sample of high school girls and anonymously asks them 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 |
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