In this exercise you will investigate the relationship between birth weight and smoking during pregnancy. The following table contains data for a random sample of babies born in Pennsylvania in 1989. The data includes the baby's birth weight together with various characteristics of the mother, including whether she smoked during her pregnancy. Download the data from the table by clicking the download table icon. A detailed description of the variables used in the data set is available here ④. Use a statistical package of your choice to answer the following questions. What is the average value of Birthweight for all mothers in the sample? The average value of Birthweight for all mothers in the sample is 3211.81 grams. (Round your response to three decimal places) What is the average value of Birthweight for mothers who smoke? The average value of Birthweight for mothers who smoke is 3117.705 grams. (Round your response to three decimal places) What is the average value of Birthweight for mothers who do not smoke? The average value of Birthweight for mothers who do not smoke is 3359 grams. (Round your response to three decimal places) Use the data in the sample to estimate the difference in average birth weight for smoking and nonsmoking mothers. The difference in average birth weight for smoking and nonsmoking mothers is (Round your response to three decimal places) grams. What is the standard error for the estimated difference? The standard error for the estimated difference is grams. (Round your response to three decimal places) Construct a 95% confidence interval for the difference in the average birth weight for smoking and nonsmoking mothers. The 95% confidence interval for the difference in the average birth weight for smoking and nonsmoking mothers is [, ] grams. ||||grams. (Round your response to three decimal places) Run a regression of Birthweight on the binary variable Smoker. Which of the following is true about the estimated slope and intercept? (Check all that apply) A. The estimated slope is the expected decrease in birth weight for every additional cigarette a mother smokes. B. The estimated intercept is the average birth weight for nonsmoking mothers. ☐ C. The estimated intercept plus the estimated slope is the average birth weight for smoking mothers. D. The estimated slope is the difference in average birth weight for smoking and nonsmoking mothers. Explain how the SE (B₁) is related to the standard error of the estimated difference in average birth weight for smoking and nonsmoking mothers. A. SE (1)₁) is equal to the standard error of the estimated difference in average birth weights for smoking and nonsmoking mothers if we assume heteroskedasticity. B. SE (B₁) is equal to the standard error of the estimated difference in average birth weights for smoking and nonsmoking mothers if we assume homoskedasticity. C. SE (B₁) is greater than the standard error of the estimated difference in average birth weights for smoking and nonsmoking mothers. D. SE (B³₁) is less than the standard error of the estimated difference in average birth weights for smoking and nonsmoking mothers. Construct a 95% confidence interval for the effect of smoking on birth weight using heteroskedasticity-robust standard errors. The 95% confidence interval for the effect of smoking on birth weight is (Round your response to three decimal places) grams. 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 u; has a conditional mean zero, given Smoking (X;)? A. Yes. B. No.