please show all the steps and rules

Spring 2022 STAT361 Dr. Reza Pokya STAT 361 Homework #2 (Chapter 5: Stratified Random Sampling) Due Saturday, March, 26, 2021 A school desires to estimate the average score that may be obtained on a reading comprehension exam for students in the sixth grade. The school's students are grouped into three tracks, with the fast learners in track I, the slow learners in track III, and the rest in track 11. TRACKI Fast learners TRACK II The rest TRACK III Slow learners The school decides to stratify on tracks because this method should reduce the variability of test scores. The sixth grade contains 55 students in track 1, 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 = 14, n = 20, and ng = 16 from tracks I, II, and III. The test is administered to the sample of students; the results are given in the following table. N=80+65+55=200 Spring 2022 STAT 361 Dr. Reza Pokyori n = 16 Grade 6 student's test results for three tracks Track 1 Track 11 Track III N = 55 N2 = 80 N3 = 65 n = 14 n2 = 20 80 91 85 72 42 53 92 90 82 81 32 14 68 81 48 53 36 61 85 62 75 59 31 31 72 79 53 68 65 42 87 61 73 52 29 30 85 83 65 71 43 39 78 61 19 32 49 59 69 42 628 14 b67 599 a. Estimate the average score for the sixth grade, and place a bound on the error of estimation. 1295 Construct parallel box plots for these data and comment on the patterns you see. Do you think there could be a problem in placing students in tracks? Estimate the difference in average scores between track I and track Il students. Are track I students significantly better, on the average, than track Il students? d. Find the sample size required to estimate the average score, with a bound of four points on the error of estimation. Use proportional allocation. P22