Question

to estimate the percentage of defects in a recent manufacturing batch, a quality-control manager selects every twentieth widget that comes off the assembly line, starting with the tenth, until he obtains a sample of sixty widgets. what type of sampling method is used? cluster, systematic, simple random, convenience, stratified

Explanation:

1. Recall the definitions of each sampling method:

• Cluster sampling: Divides the population into clusters and randomly selects some clusters. This is not the case here as we are not selecting clusters.
• Systematic sampling: Selects every \( k \)-th element from the population after a random start. Here, the manager selects every 20th widget starting from the 10th, which fits the systematic sampling definition (fixed interval \( k = 20 \) with a start point).
• Simple random sampling: Each element has an equal chance of being selected randomly, without a fixed interval. This is not the case here.
• Convenience sampling: Selects the most convenient elements, which is not what's happening here (a fixed interval is used).
• Stratified sampling: Divides the population into strata and samples from each stratum. There's no stratification here.

Answer:

systematic