From a list of 468 small 2-year colleges a simple random sample of 100 colleges was drawn. The sample contained 54 public and 46 private colleges. Data for number of students (y) and number of teachers (x) are shown below. E(y) E (x) n 31,281 13,707 2,024 1,075 Public 54 Private 46 ) E (yx) E(x?) 1,729,349 431,041 111,090 33,119 Public 29,881,219 6,366,785 Private (a) For each type of college in the population, estimate the ratio (number of students)/(number of teachers). (b) Compute the standard errors of your estimates. (c) For the public colleges, find 90% confidence limits for the student/teacher ratio in the whole population.