Suppose you collect data from a survey on wages, education, experience, marital status, and gender. In addition, you ask for information about marijuana usage. The original question asked is: "On how many separate occasions last month did you smoke marijuana?" Write a model that would allow you to test whether drug usage has different effects on wages for men and women. How would you test that there are no differences on the effects of drug usage for men and women? Suppose you think it is better to measure marijuana usage by putting people into one of four qualitative categories: nonuser, light user, moderate user, and heavy user. Now write a model that allows you to estimate the effects of marijuana usage on wage. Using the model in part above, explain in detail how to test the null hypothesis that marijuana usage has no effect on wages earned. Be specific in describing the type of statistic(s) you would employ and how they would be constructed. What are some potential problems with making causal conclusions or inferences about the effects of marijuana use on wages using survey data as described above? Explain how you might use this survey data to predict the difference in the probability of marijuana use between married and single people.