a. In the sample: i. What is the average value of Birthweight for all mothers? ii. For mothers who smoke? iii. For mothers who do not smoke? b. i. Use the data in the sample to estimate the difference in average birth weight for smoking and nonsmoking mothers. ii. What is the standard error for the estimated difference in (i)? ili. Construct a 95% confidence interval for the difference in the average birth weight for smoking and nonsmoking mothers. c. Run a regression of Birthweight on the binary variable Smoker. i. Explain how the estimated slope and intercept are related to your answers in parts (a) and (b). ii. Explain how the SE(1) is related to your answer in b (ii). iii. Construct a 95% confidence interval for the effect of smoking on birth weight. d. Do you think smoking is uncorrelated with other factors that cause low birth weight? That is, do you think that the regression error term - say Hi - has a conditional mean of 0 given Smoking (Xi)?A B C D E F G H I J K birthweight birthweight 1253 3459 Mean 3382. 933667 x bar 85 2920 Standard Error 10. 81136573 population s. d. /sqrt (n) 10. 81136573 2600 Median 3420 3742 Mode 3430 3420 Standard Deviation 592. 1628888 S 5 83. 36666667 86. 6333 2325 Sample Variance 350656. 8869 4536 Kurtosis 2. 553796071 2850 Skewness -0. 826292072 2948 Range 5330 3002 Minimum 425 3600 Maximum 5755 3175 Sum 10148801 4082 Count 3000 n 36 3714 Confidence Level (95. 21. 19844286 margin of error 21. 19027683 p (z