# 315 Balance Sheet

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Four research participants take a test of manual dexterity (high scores mean better dexterity) and an anxiety test (high scores mean more anxiety). The scores are as follows: Person Dexterity Anxiety 1 1 10 2 1 8 3 2 4 4 4 -2 a. Make a scatter diagram of the scores b. Describe in words the general pattern of correlation, if any c. Figure the correlation coefficient d. Figure whether the correlation is statistically significant (use the .05 significance level, two-tailed) e. Explain the logic of what you have done, writing as if you are speaking to someone who has never heard of correlation (but who does understand the mean, deviation scores, and hypothesis testing) f. Give three logically possible directions of causality, indicating for each direction whether it is a reasonable explanation for the correlation in light of the variables involved (and why) Dexterity Score (x) Anxiety Score (y)
1 10
1 8
2 4
4 -2 (a) Scatter Graph:

(b) It appears from the scatter diagram that there is a negative correlation between dexterity and anxiety. Higher the dexterity of a person, lower is her anxiety. This is only to be expected because more skills a person has, more confident she is and therefore less prone to being anxious. (c) R = -0.9800 and R^2 = 0.9603
We see that R = -0.98, which is close to -1, indicating a high degree of negative correlation between dexterity and anxiety. R^2 = 0.9603, which implies that 96.03% of the variation in anxiety can be explained by the variation in dexterity. (d) Hypothesis Testing:
H0: There is no correlation between the dexterity score and the anxiety score, that is, β = 0
Ha: The dexterity score and anxiety score are correlated, that is, β ≠ 0. From the Regression output, we see that the p-...

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