7. For the same population, calculate $2 for all simple random samples of size 3 and verify that E(s?) = $2. 8. From a list of 468 small 2-year colleges a simple random sample of 100 colleges was drawn. The sample contained 54 public and 45 private colleges. Data for number of students (y) and number of teachers (x) are shown below. E(y) E(1) Public 54 31,281 2,024 Private 46 13,707 1,075 Public 29,881,210 1,729,349 11,090 Private 6,366,785 431,041 33,119 (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. 9. For the public colleges, estimate the total number of teachers (a) given that the total number of public colleges in the population is 251 . (b) without knowing this figure In each case compute the standard error of your estimate 10. Two dentists A and B make a survey of the state of the teeth of 200 children in a village . Dr . A selects a simple random sample of 20 children and counts the number of decayed teeth for each child, with the following results. Number of decayed 0 1 2 3 4 5 8 9 10 teeth /child Number of children 8 4 2 2 Dr . B, using the same dental techniques , examines all 200 children , recording merely those who have no decayed teeth. He finds 60 children with no decayed teeth. Estimate the total number of decayed teeth in the village children, (a) using A's results only, (b) using both A's and B's results