On November 4, 2008, California voters approved Proposition 2. The proposition (animal welfare law henceforth) requires egg-laying hens to be given enough space to "turn around freely, lie down, stand up, and fully extend their limbs." While the animal welfare law did not specifically mandate the use of cage-free facilities, it effectively made conventional cage eggs illegal. Since the price of cage-free eggs was about 80% higher than conventional eggs, the measure worked as a catalyst for the increased availability of cage-free eggs in California. Against this backdrop, a study was conducted to see the impact of California's animal welfare on cage-free egg prices. Cage-free egg prices at individual stores were recorded at two points (before and after the law took effect) in the CSV dataset called egg.csv.' The data includes stores in California as well as stores outside California. We will refer to stores in California as the treatment group (the treatment being the change in animal welfare law) and refer to stores outside California as the control group. The 'ca' column in the dataset indicates whether the store is in the control group (0) or in the treatment group (1). The 'prop' column indicates whether the observation is recorded before the animal welfare law went into effect (0) or after the law went into effect (1). (Note: At the end of this document, you will find an appendix that thoroughly explains the conceptual idea behind this question. I recommend you read the appendix before attempting to solve the following question, as it will give you a better understanding of the general concept.) (a) Looking only at the stores in the treatment group (California), conduct a test to see whether prices of cage-free eggs after the law took effect are higher than before the law took effect. Can one conclude whether or not the law had an effect on prices based on this test? Discuss why/why not? (Hint: In SAS, you will need to reformat the data to be able to run the relevant test.) (b) Now, considering that there is indeed a control group of stores in locations where the law was not passed, conduct a test to compare the prices in the treatment and in control stores AFTER the law was passed. Can one conclude whether or not the law had an effect on prices based on this test? Discuss why/why not? (c) Conduct a test to check whether the price levels in the treatment and in control stores BEFORE the law was passed were similar or different. What do you learn from this analysis? (d) Conduct a test comparing whether the change in prices after the law was passed (compared to before the law was passed) is higher in the treatment stores than in the control stores.