AP Stats Sampling Methods and Design 2 — Questions and Answers
Question 1: A researcher divides a city into neighborhoods and randomly selects 5 neighborhoods, then surveys every household in those neighborhoods. This is an example of:
- Stratified random sampling
- Cluster sampling (Correct answer)
- Systematic sampling
- Multistage sampling
Correct answer: Cluster sampling
Cluster sampling selects entire groups (clusters) rather than individuals, then includes all members of selected clusters.
Question 2: Which of the following is the primary advantage of stratified random sampling over simple random sampling?
- It requires a smaller sample size
- It eliminates all sampling bias
- It ensures representation from every subgroup (Correct answer)
- It is easier to implement in practice
Correct answer: It ensures representation from every subgroup
Stratified sampling guarantees representation from each defined stratum, reducing variability and ensuring subgroups are not accidentally underrepresented.
Question 3: A teacher numbers students 1–30 and selects every 5th student starting from student #3. Which students are selected?
- 3, 8, 13, 18, 23, 28 (Correct answer)
- 5, 10, 15, 20, 25, 30
- 3, 6, 9, 12, 15, 18
- 1, 6, 11, 16, 21, 26
Correct answer: 3, 8, 13, 18, 23, 28
Starting at 3 and selecting every 5th: 3, 8, 13, 18, 23, 28 — this is systematic sampling.
Question 4: Undercoverage bias occurs when:
- The sample size is too small
- Some members of the population have no chance of being selected (Correct answer)
- Respondents give inaccurate answers
- The sampling interval is not constant
Correct answer: Some members of the population have no chance of being selected
Undercoverage happens when parts of the population are excluded from the sampling frame, making those groups unable to be selected.
Question 5: A polling company calls landline phone numbers to survey voters. Which bias is most likely introduced?
- Response bias
- Voluntary response bias
- Undercoverage bias (Correct answer)
- Question wording bias
Correct answer: Undercoverage bias
Using only landlines excludes people who only have cell phones, creating undercoverage of that demographic.
Question 6: In an experiment, confounding occurs when:
- The sample size is insufficient to detect differences
- An extraneous variable is associated with both the treatment and the response (Correct answer)
- Subjects are not randomly assigned to treatment groups
- The placebo effect influences the control group
Correct answer: An extraneous variable is associated with both the treatment and the response
A confounding variable is linked to both the explanatory variable and the response variable, making it impossible to isolate the treatment's effect.
Question 7: Which sampling method would be MOST appropriate to estimate the average income of households in a county that contains both urban and rural areas?
- Simple random sample from all households
- Stratified random sample by urban/rural classification (Correct answer)
- Convenience sample from the county seat
- Voluntary response survey posted online
Correct answer: Stratified random sample by urban/rural classification
Stratified sampling by urban/rural ensures both subgroups are proportionally represented, which is critical when the variable of interest (income) differs between strata.
AP Stats Sampling Methods and Design 2
A researcher divides a city into neighborhoods and randomly selects 5 neighborhoods, then surveys every household in those neighborhoods.
This is an example of: