6. A school desires to estimate the average score that would be obtained on a reading comprehension exam for students in the sixth grade. The school has students divided into three tracks, with the fast learners in track I and the slow learners in track III. It was decided to stratify on tracks since this method should reduce variability of test scores. The sixth grade contains 55 students in track I, 80 in track II, and 65 in track III. A stratified random sample of 50 students is proportionally allocated and yields simple random samples of n₁ = 14, n₂ = 20, y n3 = 16 from tracks I, II, and III, respectively. The test is administered to the sample of students with the following results: Track I 80 68 72 85 90 62 61 92 85 87 91 Track II 85 48 53 65 81 49 79 83 72 53 68 109 71 59 82 75 73 78 69 1 59 52 1 2 81 61 42 Track III 42 36 65 43 53 61 42 39 32 31 29 19 14 31 30 32 Estimate the average score for the sixth grade, and place a bound on the error of estimation. Answer: Mean = 59.99; Error = 3.032
6. A school desires to estimate the average score that would be obtained on a reading comprehension exam for students in the sixth grade. The school has students divided into three tracks, with the fast learners in track I and the slow learners in track III. It was decided to stratify on tracks since this method should reduce variability of test scores. The sixth grade contains 55 students in track I, 80 in track II, and 65 in track III. A stratified random sample of 50 students is proportionally allocated and yields simple random samples of n 1= 14, n 2= 20, y n3 = 16 from tracks I, II, and III, respectively. The test is administered to the sample of students with the following results:
Estimate the average score for the sixth grade, and place a bound on the error of estimation.
（Answer: Mean = 59.99; Error = 3.032）
7. Suppose the average test score for the class in Exercise 6 is to be estimated again at the end of the school year. The cost of sampling are equal in all strata, but the variances differ. Find the optimum (Neyman) allocation of a sample of size 50 using the data in Exercise 6 to approximate the variances.
（Answer: n 1= 11; n 2= 21; n 3= 18）
8. Using the data in Exercise 6, find the sample size required to estimate the average score with a bound of 4 points on the error of estimation. Use proportional allocation.
（Answer: n = 33）
9. Repeat Exercise 8 using Neyman allocation. Compare the result with the answer to Exercise 8.
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