Problem 3. [130 pts] We use fast-food restaurant data in New Jersey and Pennsylvania. The survey was conducted in August-September 1992, and the random sample has 410 stores. This data set is named minwage.dta, including the starting hourly wage, food prices, franchise name, location, the number of employees, etc. 1. [10 pts] Generate the total number of employees variable using the number of full-time and part-time workers. 2. [10 pts] Estimate the percentage of full-time employees in New Jersey and Pennsylvania. 3. [10 pts] What are the estimated probability distributions of store types (Burger King, KFC, Roy Rogers, Wendys) in New Jersey and Pennsylvania? 4. [10 pts] Estimate the correlation coefficient of two random variables: the number of full-time and part-time employees. Interpret the meaning of your estimate. 5. [10 pts] You want to take a single-variable linear regression Employeesi = 0 + 1Starting Wagei + ui. (1) What are the least squares estimates for 0 and 1? How do you interpret the estimates? 6. [10 pts] Take the regression for equation (1) with specific groups of stores: stores in New Jersey and Pennsylvania. What is the estimated difference in the expected number of total employees between the two states? 7. [10 pts] Do you accept/reject the null hypothesis that the employment levels in New Jersey and Pennsylvania are the same? 8. [10 pts] In early 1990 the New Jersey legislature enacted parallel increases in the state mini- mum wage for 1990 and 1991 and an increase to $5.05 per hour effective April 1, 1992. How do you interpret the result of your estimation in part 5 in the context of the minimum wage increase?

9. [20 pts] Suppose you are currently living in southern New Jersey and working at KFC. You work 8 hours daily and pay for a medium soda, small fries, and an entree daily. How much are you expected to earn every day? 10. [30 pts] Now you have a chance to move to the northeast suburbs of Philadelphia. Assuming that your consumption pattern is the same, would you take the opportunity to move to a new place?