Are young New Zealand women having their children at a later age than previous generations?

(a) Out of the 314 women in the age group 25-29, 136 report having given birth to their first child before the age of 25. Find the posterior distribution of π1, the proportion of New Zealand women in that age group who have given birth before age 25. (Use a uniform prior for π1.)

(b) Out of the 219 women in the age group 50-54, 135 report having given birth to their first child before age 25. Find the posterior distribution of

π2, the proportion of New Zealand women in that age group who have given birth before age 25. (Use a uniform prior for π2.)

(c) Find the approximate posterior distribution of π1 − π2.

(d) Test the hypothesis H :0: π1 − π2 ≥ 0 versus H1 : π1 − π2 < 0 in a Bayesian manner at the 1% level of significance. Can we conclude that New Zealand women in the generation aged 25-29 have had their first child at a later age than New Zealand women in the generation aged 50-54?