The variable smoker is a binary variable equal to one if an individual smokes. It has been argued that workplace smoking bans induce smokers to quit smoking by reducing their opportunities to smoke. Using data on a sample of 10,000 U.S. workers, we estimate both a linear probability model and a probit model for smoker, with smkban, age, hsdrop, hsgrad, colsome, colgrad, black, and female as explanatory variables, where smkban=1 if there is workplace smoking ban age = workers age, in years hsdrop = 1 if high school dropout hsgrad = 1 if high school graduate colsome = 1 if some college education colgrad = 1 if college graduate black = 1 if black hispanic = 1 if hispanic female = 1 if female. The omitted education status is Masters degree or higher. The results are as shown in the table:

a. (5) Using the linear probability model (1), find the difference in the probability of smoking between workers affected by a workplace smoking ban and workers not affected by a workplace smoking ban. Is this difference statistically significant? Report a bound on the p-value.

b. (6) Using the linear probability model (2), find the difference in the probability of smoking between workers affected by a workplace smoking ban and workers not affected by a workplace smoking ban. Suggest a reason, based on the estimated models, explaining the change in the estimated effect of a working ban between (a) and (b).

c. (4) Interpret the coefficients of the binary variables related to the level of education in the linear probability model (2).

d. (5) Mr. A is white, non-Hispanic, 20 years old, and a high school dropout. Using the probit model, and assuming that Mr. A is not subject to a workplace smoking ban, calculate the probability that Mr. A smokes. Carry out the calculation again assuming that he is subject to a workplace smoking ban. What is the effect of smoking ban on the probability of smoking?

e. (5) Repeat (d) for the linear probability model (2). Do the probit and linear probability model results differ?

The results are as shown in the table: Regression Probit intercept smkban age age? hsdrop Linear Probability Linear Probability Model (1) Model (2) 0.290 -0.014 (0.045) (0.041) -0.078 -0.047 (0.009) (0.009) 0.0097 (0.0018) -0.00013 (0.00002) 0.323 (0.019) 0.233 (0.013) 0.164 (0.013 0.045 (0.012) -0.028 (0.016) -0.105 (0.014) -0.033 (0.009) hsgrad -1.735 (0.053) -0.159 (0.029) 0.035 (0.007) -0.00047 (0.00008) 1.142 (0.072) 0.883 (0.060) 0.677 (0.061) 0.235 (0.065) -0.084 (0.053) -0.338 (0.048) -0.112 (0.028) colsome colgrad black hispanic female The results are as shown in the table: Regression Probit intercept smkban age age? hsdrop Linear Probability Linear Probability Model (1) Model (2) 0.290 -0.014 (0.045) (0.041) -0.078 -0.047 (0.009) (0.009) 0.0097 (0.0018) -0.00013 (0.00002) 0.323 (0.019) 0.233 (0.013) 0.164 (0.013 0.045 (0.012) -0.028 (0.016) -0.105 (0.014) -0.033 (0.009) hsgrad -1.735 (0.053) -0.159 (0.029) 0.035 (0.007) -0.00047 (0.00008) 1.142 (0.072) 0.883 (0.060) 0.677 (0.061) 0.235 (0.065) -0.084 (0.053) -0.338 (0.048) -0.112 (0.028) colsome colgrad black hispanic female