Question

identify the sampling technique used.

every 27th person in line to buy tickets to a concert is asked his or her age.

what type of sampling is used?

convenience
stratified
random
cluster
systematic

Explanation:

Analyze the sampling scenario

The scenario describes selecting "every 27th person in line." This represents selecting members from a larger population according to a random starting point and a fixed, periodic interval.

Match with sampling definitions

• Convenience: Selecting individuals who are easiest to reach.
• Stratified: Dividing the population into subgroups (strata) and taking a random sample from each.
• Random: Every member of the population has an equal chance of being selected.
• Cluster: Dividing the population into clusters, randomly selecting entire clusters, and surveying everyone in those clusters.
• Systematic: Selecting every \(k\)-th individual from a list or sequence.

Determine the correct technique

Selecting every 27th person is a classic application of selecting every \(k\)-th element, which is the definition of systematic sampling.

Answer:

• Convenience
• Stratified
• Random
• Cluster
• Systematic (Correct answer)