. A university consists of two colleges: Arts and Sciences1 and Engineering. The university wishes to estimate the average starting salary of its reoent graduates. Within each eollege, they select a simple random sample of recent graduates and record their starting salaries. The sample data are given below. Nh on is 5% Arts and Sciences 5401] 25 52,500 250,, Engineering seat] as eases teams [a] [4 pts} Estimate the population mean starting salary. Give a point estimate and standard error. {11) [3 ptsj Assume the above data represent a pilot study From which to design a larger study. Take the sample variances as population variances to allocate n 2 see sample units to the two strata using proportional allocation. [c] [:1 pts} Repeat part {h} but assume equal cost for sampling and calculate the optimal allocation. {d} [2 ptsj Would you recommend proportional allocation or optimal allocation? 'Nhy