Question

(a)
Samuel is interested in finding out the favorite video game of other students ​at his school.

Part A:
Samuel decides he is going to conduct a sample survey to answer ​this question.
​Explain how he could design his survey and how he ​could randomly choose those who will take the survey.

Answer 1

Outline a practical survey plan and a few ways to select students at random.

1. Define the goal and population
- Goal: estimate the favorite video game among all students at Samuel’s school.
- Population: every student enrolled at the school (specify grades included).

2. Design the questionnaire
- Ask one clear, neutral question, e.g.: “What is your single favorite video game?” (allow an “Other — please write in” and “I don’t play video games / Prefer not to answer” option).
- If you give a list of games, include an “Other” choice and avoid ordering that biases answers.
- Keep it short so students will respond.
- Pilot the question with a few students to check clarity.

3. Choose a sampling method (three good options)
- Simple random sample (SRS): get a complete roster of all students, assign each student a unique number, then use a random-number generator (e.g., random.org, Excel RAND(), or a random-number table) to pick the required count. This gives every student equal chance.
- Stratified random sample: if you want representation by grade (or by gender, class, etc.), split the roster into strata (e.g., grades 9–12), then randomly sample from each stratum proportionally (or with fixed numbers). This reduces sampling error when preferences differ by strata.
- Cluster sampling (practical in schools): randomly select a number of whole classes or homerooms and survey every student in those selected clusters. This is easier to administer but increases sampling error vs. SRS; you can compensate by selecting more clusters.

4. Decide sample size
- Larger samples give more precise estimates. For quick guidance: a few hundred students usually gives reasonable precision for school-size populations; adjust if resources limit you. Use proportional stratified sizes if using stratification.

5. Random selection methods (practical approaches)
- Using a roster: number each student 1 to N, then use a random-number generator to pick the sample.
- Using Excel/Google Sheets: add a column with =RAND() and sort by that column, then select the top n rows.
- Using a hat: write each student’s name on a slip and draw randomly (works for small schools).
- Systematic sampling: if you have an ordered list, pick a random start between 1 and k, then take every kth student (k = population size / sample size). This approximates random sampling but avoid if the roster has periodic patterns.

6. Administer the survey
- Get permission from school administration and parents if required.
- Explain purpose, voluntary participation, and confidentiality/anonymity.
- Offer a short in-class time slot or an online form (Google Form) to collect responses.
- Follow up non-respondents once or twice; record response rate.

7. Handle bias and nonresponse
- Avoid leading questions and lists that prime answers.
- If certain groups have low response rates, consider weighting results or using stratified sampling to reduce bias.
- Report the response rate and any known limitations when presenting results.

Example simple plan
- Obtain a complete student roster (N = total).
- Decide to sample 200 students.
- Use Excel: assign RAND() to each student, sort descending, select the top 200.
- Email the students a short anonymous survey link and collect answers in one week; remind once.
- Summarize percentages for each game and report margin of error.

If you tell me the school size and whether you want representation by grade, I can suggest a specific sample size and give exact steps to produce random selections.