# Testing of correlation

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## Ben is interested in flirting. He wants to know what kinds of people

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Question: Ben is interested in flirting. He wants to know what kinds of people are likely to be good (and bad) at flirting. He thinks that self-confidence will be correlated with flirting ability, but he’s not sure which way it will go. High self-confidence should make for good flirters, but if people are too self-confident, it might hurt their flirting performance. So he gives a number of students a self-confidence measure (Y) and then watches them try to flirt with people at an off-campus bar (X). Both scales range from 1 (low) to 7 (high). He records the following scores:

 Self-Confidence (X) Flirting (Y) 4 5 6 3 6 5 7 6 6 7 3 1 6 4 2 3 3 2 3 4
1. a) Compute the correlation for these scores. (SHOW YOUR WORK! Use as much space as necessary.)
2. b) What does this correlation tell us about the relationship between self-confidence and flirting ability?
3. c) What is Ben’s alternative hypothesis?
4. d) What is Ben’s null hypothesis?
5. e) What is the coefficient of determination for these scores?
6. f) How did you compute the coefficient of determination?
7. g) How many degrees of freedom are there in this example?
8. h) How did you compute the degrees of freedom? Should Ben perform a one-tailed or two-tailed test?  Why?
9. i) Assuming α = .05, what is the critical value for this example?
10. j) Is the correlation you computed statistically significant? YES  or   NO
11. k) How do you know whether or not the correlation is statistically significant?