1. When two variables are correlated, like speed and strength, we say they are associated with each other. Explain why the relationship is not necessarily causal even if the two variables are associated.
2. Provide two examples of an association between two variables where a causal relationship may make sense and one example of an association between to variables where a causal relationship does not make sense (don't use any examples from above! Come up with your own).
3. A study shows there is a positive correlation between the size of a hospital (measured by the number of beds) and the median number of days someone spends in a hospital. Should we choose a smaller hospital in order to shorten a hospital stay? Why or why not? How can we explain this relationship?
4. Imagine we surveyed 375 freshmen and sophomores about their preference for vanilla and chocolate ice-cream. 95 freshmen preferred vanilla and 85 preferred chocolate. 100 sophomores preferred vanilla and 95 preferred chocolate. Create a two-way table (use the table feature of Word or whichever writing software you use). You'll have to do some minor math. Then create table for the joint distribution and marginal distributions. Why are these tables more useful than just looking at numbers listed here?