Please complete in python using pandas, numpy, matplotlib, and seaborn packages

1a) The data for this task come from a random sample of 150 births from the birth records in the US state of North Carolina in 2004. The data contains 50 records from mothers that self-identified as having smoked on average more than 2 cigarettes per week during the pregnancy (smokers) and 100 mothers that smoked not at all or less than 2 cigarettes per week during the pregnancy.

The data frame has 150 observations with the following 9 variables:

fAge: Fathers age.

mAge: Mothers age.

weeks: Weeks at which the mother gave birth.

premature: Indicates whether the baby was premature or not.

visits: Number of hospital visits.

gained: Weight gained by mother (lbs)

weight: Birth weight of the baby (lbs)

sexBaby: Gender of the baby

smoke: Whether or not the mother self-reported to be a smoker.

a) What is the posterior probability of the H1, assuming that a-priori you had the belief that there was a 70% chance that smoking may reduce the birth weight by 0.5lb. Show clearly the formula used to calculate the posterior probability. Written answer: What is the meaning of this posterior probability? How does the meaning differ from the p-value?

b) A news outlet picks up your result, saying that "the study shows that smoking among US women causes an average decrease in birth weight of 0.4lbs." Can you draw this conclusion from the data? What are two possible problems with such claim?

Below is the dataset called births.csv:

fAge,mAge,weeks,premature,visits,gained,weight,sexBaby,smoke 31,30,39,full term,13,1,6.88,male,smoker 34,36,39,full term,5,35,7.69,male,nonsmoker 36,35,40,full term,12,29,8.88,male,nonsmoker 41,40,40,full term,13,30,9,female,nonsmoker 42,37,40,full term,0,10,7.94,male,nonsmoker 37,28,40,full term,12,35,8.25,male,smoker 35,35,28,premie,6,29,1.63,female,nonsmoker 28,21,35,premie,9,15,5.5,female,smoker 22,20,32,premie,5,40,2.69,male,smoker 36,25,40,full term,13,34,8.75,female,nonsmoker 27,19,32,premie,5,32,6.5,female,nonsmoker 35,34,40,full term,15,20,7.44,male,nonsmoker 25,19,41,full term,13,47,8.38,male,smoker 36,33,38,full term,10,20,6,male,nonsmoker 27,27,39,full term,11,5,7.81,male,smoker 24,23,38,full term,13,22,7.81,female,nonsmoker 33,40,36,premie,13,23,7.81,female,nonsmoker 25,23,40,full term,10,30,7.31,male,nonsmoker 28,27,33,premie,6,18,4.75,male,smoker 25,22,34,premie,10,20,3.75,male,nonsmoker 35,31,37,full term,12,37,8.06,female,nonsmoker 33,38,32,premie,10,16,2.19,female,smoker 32,26,42,full term,15,30,7.38,male,smoker 29,30,39,full term,10,43,6.88,female,nonsmoker 24,22,40,full term,16,34,6.88,female,smoker 25,25,38,full term,19,13,7.63,female,nonsmoker 34,33,43,full term,13,25,9.13,male,smoker 33,20,39,full term,15,70,7.38,female,smoker 32,28,37,full term,13,35,8.25,female,nonsmoker 28,26,39,full term,15,45,7.19,female,nonsmoker 27,27,39,full term,14,31,7.56,female,nonsmoker 25,21,36,premie,15,10,6.81,male,nonsmoker 21,24,38,full term,16,50,3.75,female,nonsmoker 26,25,38,full term,11,27,8.75,male,nonsmoker 33,30,37,full term,10,57,6.56,male,nonsmoker 27,25,40,full term,11,26,7.44,male,nonsmoker 34,25,39,full term,5,37,6,female,smoker 29,21,39,full term,18,13,7.75,female,nonsmoker 33,30,39,full term,9,42,7.81,male,smoker 39,24,39,full term,6,30,5.8,female,smoker 24,23,42,full term,9,22,8.81,male,nonsmoker 29,26,39,full term,14,65,7.75,female,smoker 35,28,38,full term,10,25,6.88,male,nonsmoker 27,22,35,premie,12,30,4.69,male,nonsmoker 33,25,35,premie,15,18,6.75,male,nonsmoker 27,22,39,full term,12,30,6.94,female,smoker 30,25,35,premie,15,40,5.5,male,smoker 23,23,44,full term,4,55,6.8,female,smoker 21,22,40,full term,10,85,5.81,male,nonsmoker 22,32,37,full term,8,30,6.81,female,nonsmoker 34,34,38,full term,11,23,7.25,male,nonsmoker 22,22,39,full term,14,29,7.19,female,nonsmoker 35,31,40,full term,10,45,8,female,nonsmoker 25,26,39,full term,12,40,8.38,male,nonsmoker 22,26,39,full term,12,31,7.31,male,smoker 22,34,39,full term,12,57,9.69,male,nonsmoker 40,40,38,full term,13,38,7.31,male,nonsmoker 24,18,37,full term,8,25,6.19,male,smoker 42,38,41,full term,15,35,10.13,female,nonsmoker 30,28,39,full term,13,0,7.5,female,nonsmoker 35,31,40,full term,15,32,6.25,male,nonsmoker 39,27,39,full term,12,58,8.56,male,smoker 28,18,41,full term,10,11,6.5,female,nonsmoker 29,29,44,full term,12,51,8.5,male,nonsmoker 28,24,39,full term,11,23,7.5,female,nonsmoker 33,35,38,full term,10,20,5.2,female,smoker 29,31,36,premie,8,42,5.32,male,smoker 19,20,34,premie,13,6,4.5,male,nonsmoker 21,19,39,full term,11,48,7.3,female,smoker 43,31,41,full term,5,20,6.7,female,smoker 33,27,41,full term,15,38,7.8,male,smoker 27,21,41,full term,8,26,5.94,female,nonsmoker 29,30,39,full term,15,44,7.2,male,smoker 21,20,37,full term,10,26,5.38,female,smoker 23,16,40,full term,4,12,6,female,nonsmoker 34,34,37,full term,17,35,6.88,female,nonsmoker 26,26,41,full term,10,68,9.31,male,nonsmoker 22,22,40,full term,13,0,6.5,male,smoker 31,32,38,full term,6,27,6.75,female,nonsmoker 39,37,38,full term,5,45,5.13,male,nonsmoker 36,37,38,full term,3,23,7.5,male,smoker 34,36,38,full term,4,25,7.2,male,smoker 33,32,33,premie,10,60,5.06,male,nonsmoker 30,24,41,full term,12,40,8.13,male,smoker 30,29,39,full term,14,30,5.38,male,nonsmoker 27,24,40,full term,11,8,7.69,female,nonsmoker 23,23,41,full term,14,19,7.88,female,nonsmoker 24,21,41,full term,13,40,7.88,female,nonsmoker 34,29,39,full term,15,24,8.25,female,nonsmoker 32,25,41,full term,13,50,7.75,female,nonsmoker 26,25,40,full term,10,25,7,male,nonsmoker 45,41,33,premie,13,0,5.69,female,nonsmoker 26,23,42,full term,14,23,6.75,male,nonsmoker 25,34,41,full term,10,35,8.19,female,nonsmoker 24,19,40,full term,12,36,8.19,male,nonsmoker 35,31,39,full term,15,35,7.44,male,nonsmoker 35,36,38,full term,18,37,8.25,male,nonsmoker 28,25,40,full term,7,31,9.19,male,nonsmoker 34,31,40,full term,14,44,7.5,female,nonsmoker 35,33,40,full term,16,30,6.81,male,nonsmoker 30,25,40,full term,12,35,8.13,male,nonsmoker 26,20,41,full term,16,21,6.9,female,smoker 24,22,39,full term,12,32,8.38,male,nonsmoker 23,26,38,full term,14,40,8,male,smoker 34,27,39,full term,16,24,8.88,male,smoker 22,20,40,full term,17,39,9.06,male,smoker 26,17,38,full term,11,30,9.5,female,nonsmoker 22,18,40,full term,12,13,8.75,male,nonsmoker 34,33,39,full term,10,40,8.06,male,nonsmoker 20,23,39,full term,15,56,7.31,male,smoker 21,16,38,full term,15,75,7.56,male,smoker 22,20,38,full term,8,45,7.44,female,nonsmoker 32,35,38,full term,17,55,7.5,female,nonsmoker 37,35,40,full term,16,32,7.31,female,nonsmoker 36,30,39,full term,11,21,7.88,male,nonsmoker 31,23,44,full term,14,40,6.81,male,nonsmoker 20,20,37,full term,12,22,5.94,female,nonsmoker 46,39,38,full term,10,35,6.75,male,smoker 23,25,37,full term,8,53,7.69,female,nonsmoker 28,21,38,full term,12,40,7.38,male,nonsmoker 25,19,40,full term,16,37,7.94,male,smoker 33,24,39,full term,8,22,5,male,smoker 17,20,39,full term,16,35,5.63,female,nonsmoker 27,23,43,full term,15,30,7.81,female,nonsmoker 33,27,41,full term,14,58,8,male,nonsmoker 22,18,33,premie,7,40,1.69,male,smoker 26,23,38,full term,5,28,7.19,female,nonsmoker 37,33,36,premie,11,15,6.31,male,smoker 32,24,39,full term,8,23,6.88,male,smoker 24,22,42,full term,7,21,6.5,female,nonsmoker 17,17,29,premie,4,10,3.5,female,nonsmoker 18,15,37,full term,12,76,8.44,male,nonsmoker 24,20,41,full term,16,35,7.19,male,nonsmoker 22,21,41,full term,12,32,8.38,male,nonsmoker 20,17,40,full term,17,38,7.19,female,nonsmoker 25,22,39,full term,12,27,6.31,female,smoker 33,33,38,full term,15,60,6.56,male,nonsmoker 23,21,40,full term,15,38,7.63,female,nonsmoker 36,28,39,full term,15,40,8.38,male,nonsmoker 31,29,41,full term,12,30,7.69,male,smoker 23,23,36,premie,2,27,5.88,female,nonsmoker 22,19,39,full term,7,0,7.31,male,smoker 47,24,40,full term,12,46,6.88,male,nonsmoker 32,35,37,full term,10,25,5.63,male,smoker 30,29,38,full term,17,55,7,female,nonsmoker 25,17,40,full term,15,20,7.63,female,nonsmoker 38,37,39,full term,5,20,6.5,male,smoker 31,32,37,full term,12,22,6,female,nonsmoker 33,28,41,full term,10,30,8.13,male,nonsmoker 38,37,26,premie,5,25,3.63,male,nonsmoker