I'lrlanj,r liberal arts colleges and ether organizations have been promoting science majors in recent years because of their value on the job market. One wishes to evaluate whether such promotion has anyr effect on student major preference. A college student Clara is interested in this question and collects data from three liberal arts colleges. Table T4. Data from three liberal arts colleges on science majors in 2005 and 2015. Year Science Non-Science 2005 204 1400 2015 43? 1495 Suppose one uses the parameter o = p2015 - P20os to measure the difference in proportions. Use simulation from the posterior distribution to answer the question "have the proportions of science majors changed from 2005 to 2015?". [Hint: simulate a vector $2005 of posterior samples of p2005 and another vector $2015 of posterior samples of p21s (make sure to use the same number of samples) and subtract $2005 from $2015 which yields a vector of simulated values from the posterior of 6.]