Suppose the average test score
Suppose the average test score for the class in Exercise 5.6 is to be estimated again at the end of the school year. The costs 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 5.6 to approximate the variances.
Exercise 5.6
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 II. 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 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, and n3 = 16 from tracks I, II, and III. The test is administered to the sample of students; the results are available via a link from electronic Section 5.0.
a. Estimate the average score for the sixth grade, and place a bound on the error of estimation.
b. 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?
c. Estimate the difference in average scores between track I and track II students. Are track I students significantly better, on the average, than track II students?
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Posted 29 Apr 2017 08:04 AM
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