Question 19 of my final exam for Design and Analysis of Sample Surveys

19. A survey is taken of students in a metropolitan area. At the first stage a school is sampled at random. The schools are divided into two strata: 20 private schools and 50 public schools are sampled. At the second stage, 5 classes are sampled within each sampled school. At the third stage, 10 students are sampled within each class. What is the probability that any given student is sampled? Express this in terms of the number of students in the class, number of classes in the school, and number of schools in the area. Define appropriate notation as needed.

Solution to question 18

From yesterday:

18. A survey is taken of 100 undergraduates, 100 graduate students, and 100 continuing education students at a university. Assume a simple random sample within each group. Each student is asked to rate his or her satisfaction (on a 1–10 scale) with his or her experiences. Write the estimate and standard error of the average satisfaction of all the students at the university. Introduce notation as necessary for all the information needed to solve the problem.

Solution: Let N.1,N.2,N.3 be the population sizes, y.bar.1,y.bar.2,y.bar.3 be the sample averages, s.1,s.2,s.3 be the sample standard deviations within each stratum. Then the estimate is (N.1*y.bar.1+N.2*y.bar.2+N.3*y.bar.3)/(N.1+N.2+N.3) and the se is sqrt ((N.1/(N.1+N.2+N.3))^2*s.1^2/100 + (N.2/(N.1+N.2+N.3))^2*s.2^2/100 + (N.3/(N.1+N.2+N.3))^2*s.3^2/100).

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  1. Pingback: Question 20 of my final exam for Design and Analysis of Sample Surveys « Statistical Modeling, Causal Inference, and Social Science

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