Suppose we want to estimate the average weight of children in a particular schoo

Question

Suppose we want to estimate the average weight of children in a particular school district. The district contains 15 elementary schools, 10 middle schools, and 2 high schools. For each of the following approaches, select the best description of the sampling design, and identify whether the sampling scheme ensures that the probability of being included is necessarily the same for every student.

A. List all the students in the school district. Average the weights of every 50th student on the list.

(Q5)  ? A: a simple random sample B: a systematic random sample C: a stratified random sample D: a random cluster sample E: a random stratified cluster sample F: a multistage random sample G: a multistage random cluster sample H: a random stratified multistage cluster sample I: a systematic sample J: another non-probability sample

B. Take a simple random sample of 5 schools in the district. For each school in the sample, list all the homerooms. Take a simple random sample of 3 homerooms from each school in the sample. For each homeroom in the sample, list the students. Take a simple random sample of 10 students from each homeroom in the sample. List their weights. Combine the lists and average the results.

(Q7)  ? A: a simple random sample B: a systematic random sample C: a stratified random sample D: a random cluster sample E: a random stratified cluster sample F: a multistage random sample G: a multistage random cluster sample H: a random stratified multistage cluster sample I: a systematic sample J: another non-probability sample

C. List all the schools in the school district. For each school, list all the teachers at the school; sort them alphabetically within each school. For each school, list the weights of the students of the teacher who is first on that school's sorted teacher list. Combine the lists and average the results.

(Q9)  ? A: a simple random sample B: a systematic random sample C: a stratified random sample D: a random cluster sample E: a random stratified cluster sample F: a multistage random sample G: a multistage random cluster sample H: a random stratified multistage cluster sample I: a systematic sample J: another non-probability sample

D. Take a simple random sample of 5 schools in the district. For each school in the sample, list the weights of all the students. Combine the lists and average the result.

(Q11)  ? A: a simple random sample B: a systematic random sample C: a stratified random sample D: a random cluster sample E: a random stratified cluster sample F: a multistage random sample G: a multistage random cluster sample H: a random stratified multistage cluster sample I: a systematic sample J: another non-probability sample

1 answer for each

Explanation / Answer

A. List all the students in the school district. Average the weights of every 50th student on the list.
The best description of the sampling design is a systematic random sample the sampling scheme ensures that the probability of being included is necessarily the same for every 50 th student.
B. Take a simple random sample of 5 schools in the district. For each school in the sample, list all the homerooms. Take a simple random sample of 3 homerooms from each school in the sample. For each homeroom in the sample, list the students. Take a simple random sample of 10 students from each homeroom in the sample. List their weights. Combine the lists and average the results.
The best description of the sampling design is a stratified random sample because within stratium samples are as homogenious as possible and the sampling scheme ensures that the probability of being included is necessarily the same for every student because from each stratum we select 10 students.
C. List all the schools in the school district. For each school, list all the teachers at the school; sort them alphabetically within each school. For each school, list the weights of the students of the teacher who is first on that school's sorted teacher list. Combine the lists and average the results and the sampling scheme ensures that the probability of being included is necessarily the same for every student.

The best description of the sampling design is a simple random sample because list the weights of the students of the teacher who is first on that school's sorted teacher list and and the sampling scheme ensures that the probability of being included is necessarily the same.
D. Take a simple random sample of 5 schools in the district. For each school in the sample, list the weights of all the students. Combine the lists and average the result.
The best description of the sampling design is a simple random sample and the sampling scheme ensures that the probability of being included is necessarily the same.

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