Sampling Methods Statistics Worksheet

Name:

Date:

📊 Part 1: Multiple Choice Questions

1. Which of the following is an example of random sampling?

Selecting every 5th student from a class list

Using a computer to randomly select 50 students from the school database (Correct Answer)

Asking students to volunteer for a survey

Surveying only Year 10 students

2. What is the main advantage of stratified sampling?

It's the easiest method to implement

It ensures all subgroups are represented proportionally (Correct Answer)

It always produces the largest sample size

It eliminates all bias completely

3. In systematic sampling, if you have a population of 1000 and want a sample of 50, what would be your sampling interval?

10 (Correct Answer)

100

4. Which sampling methods could introduce bias? (Select all that apply)

Self-selected sampling (Correct Answer)

Convenience sampling (Correct Answer)

Random sampling

Stratified sampling

5. A researcher wants to survey students about school lunch preferences. They stand outside the canteen and ask the first 30 students they see. This is an example of:

Random sampling

Systematic sampling

Convenience sampling (Correct Answer)

Stratified sampling

✏️ Part 2: Short Answer Questions

6. Explain the difference between random sampling and systematic sampling.

Random sampling selects individuals from a population entirely by chance, ensuring every member has an equal chance of being chosen. Systematic sampling selects individuals based on a fixed interval from a randomly selected starting point.

7. A school has 400 Year 7 students, 350 Year 8 students, 300 Year 9 students, and 250 Year 10 students. If you want a stratified sample of 65 students, how many should come from each year level?

Year 7: 400/1300 * 65 = 20
Year 8: 350/1300 * 65 = 17
Year 9: 300/1300 * 65 = 15
Year 10: 250/1300 * 65 = 13

8. List two advantages and two disadvantages of self-selected sampling.

Advantages: 1) Easy to implement; 2) Participants are motivated to respond. Disadvantages: 1) May lead to bias as only those with strong opinions participate; 2) Not representative of the entire population.

9. Why might systematic sampling be problematic if there's a pattern in the population list?

If there's a pattern, systematic sampling could result in a biased sample that does not accurately represent the population, as certain groups may be overrepresented or underrepresented.

🎯 Part 3: Scenario-Based Questions

10. A local council wants to survey residents about a new park. They mail surveys to every household and ask people to return them voluntarily. Identify the sampling method and explain one major concern with this approach.

This is an example of voluntary response sampling. A major concern is that it may lead to bias, as those who feel strongly about the issue are more likely to respond, while those indifferent may not.

11. A researcher studying teenage social media use decides to survey students by selecting every 15th name from an alphabetical list of all high school students in the area. What sampling method is this, and what assumption must be true for this method to work well?

This is systematic sampling. The assumption is that the list of students is randomly ordered, so that every subgroup is equally represented.

12. Design a sampling strategy to investigate whether students prefer online or face-to-face learning. Your school has 1200 students across Years 7-12. Describe your chosen method and justify why it would produce reliable results.

I would use stratified random sampling, ensuring that each year group is represented proportionally. This method would produce reliable results as it accounts for differences in preferences across age groups.