## Question 711:

1## Answer:

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a. See the attached excel file for the scatter diagram from MegaStat and Minitab.b. We see there is a strong negative association (correlation) between dexterity and anxiety. That is, as anxiety levels increase, dexterity decreases.

c. The correlation coefficient, r, between these two variables is r = -.97996 (see the excel file for the formula =CORREL() ).

d. To test the significance of the correlation we use the t-test and just insert the values of r and the sample size (4).

| t = | rsqrt[(1—r^{2})/(N—2)] |

We get a 2-tailed p-value of .020, which is less than .05, so it is a significant correlation.

e. When we compare the deviation scores for anxiety and dexterity, we see that strong associations. Even taking into account chance fluctuations, we see a pattern by which we see high deviation scores around anxiety associated with high deviation scores with dexterity.

f. Three logically possible directions of causality are:

- Higher anxiety levels cause participants to be distracted and reduces their dexterity (most plausible). When one is distracted or anxious, it seems very reasonable to assume this will affect their performance and dexterity.
- Higher dexterity in participants leads to levels of increased anxiety (not really reasonable). It seems rather unlikely that have high dexterity makes you anxious.
- A third and unknown variable, causes increases in dexterity and is also associated with anxiety (e.g. people with attention deficit disorder). (reasonable). This is more reasonable, but more difficult to measure. It could very well be a nuisance variable like ADD is affecting both.