Final answer:
An independent t-test would be the best approach for comparing the mean scores of Republicans and Democrats on a "need dependence" questionnaire to test the hypothesis of a difference between the two groups.
Step-by-step explanation:
The most appropriate analysis to test the hypothesis that Democrats and Republicans differ with respect to the personality trait of "need dependence" would be an independent t-test. This statistical test is used when comparing the means of two independent groups to see if there is a statistically significant difference between them. In this case, 10 Republicans and 10 Democrats will have their questionnaire scores compared to evaluate the hypothesized difference in the trait of "need dependence".