b) What is the average value of Birthweight for all mothers who smoke? c] What is the average value of Birthmeight for all mothers who do not smoke? Problem 2. Use the data to estimate the difference in average birth weight for smoking and nonsmoking mothers. 3.] What is the standard error for the estimated dierence? b) Construct a 95% condence interval for the difference in the average birth weight for smoking and nonsmoking mothers. Problem 3. Run a regression of Birth-weight on the binary variable Smoker. 3.) Explain how the estimated slope and intercept are related to your answers in Problem 1 and Problem 2. b) Explain how the S E ( 31] is related to your answer in Problem 2. c] Construct a 95% condence interval for the effect of smoking on birth weight. Problem 4. Do you think that smoking is uncorrelated with other factors that cause low birth weight? That is, do you think that the regression error term has a conditional mean of [l given Smoking {Xi}