4.8 More posterior predictive checks: Let 6A and (93 be the average num ber of children of men in their 30s with and without bachelor's degrees, respectively. 60 Using a Poisson sampling model, a gamma(2,1) prior for each (9 and the data in the les menchild30bach.dat and menchildBOnobach.dat, obtain 5,000 samples of 17A and 173 from the posterior predictive dis tribution of the two samples. Plot the Monte Carlo approximations to these two posterior predictive distributions. Find 95% quantilebased posterior condence intervals for 63 6A and 173124. Describe in words the differences between the two populations using these quantities and the plots in a), along with any other results that may be of interest to you. Obtain the empirical distribution of the data in group B. Compare this to the Poisson distribution with mean 6 = 1.4. Do you think the Poisson model is a good t? Why or why not? For each of the 5,000 HBvalues you sampled, sample 713 = 218 Poisson random variables and count the number of 0s and the number of 1s in each of the 5,000 simulated datasets. You should now have two sequences of length 5,000 each, one sequence counting the number of people having zero children for each of the 5,000 posterior predictive datasets, the other counting the number of people with one child. Plot the two sequences against one another (one on the scaxis, one on the yaxis). Add to the plot a point marking how many people in the observed dataset had zero children and one child. Using this plot, describe the adequacy of the Poisson model