1. On Blackboard under the Homework folder: you can nd a zip le birthweightaip, which contains a database birthweightjmokingmsv for infant's birth weight {in grams} with an indicator equal to one if the mother smoked during pregnancy and zero, otherwise. A detailed dmcription is given in the pdf le Datamlescription. In this exercise, you will investigate the relationship between a mother smoked during pregnancy {smoker} and birth weight of infant [birthweight]l. The variable smoker takes value 1 if the mother smoked during pregnancy and 0 otherwise. {a} Assume both the birth weight of infant distribution with a mother smoked during pregnancy, and the birth weight of infant distribution without a mother smoked during pregnancy follow a normal distribution and having mean #1 and an respectively. Write down the estimators for p1 and an respectively. (b) Write down the [null and alternative} hypotheses that the difference between the average birth weight of infant with a mother smoked during pregnancy and the average birth weight of infant without a mother smoked during pregnancy is zero. Then write down test statistic for the hypothesis test {Assume the variances of the two groups are not equal) and the pvalue for the test. [c Construct a 1 o: condence interval for :11 Fn- [d [e [f Use H. to compute the sample mean and sample variance of birthweight with a Use R, to delete the variables tpre and tripre3. Use R to create a new variable logfhirthweight}. } } } 1| mother smoked during pregnancy and those without a mother smoked during pregnancy. {g} Use R to compute the test statistic and pvalue. Will you reject the null hy- pothesis at the 5% signicance level based on the pvalue'? (h) Use R to compute the 95% condence interval for in pg