A production line in a large factory produces 20,000 ballpoint pens per day. The company performs quality control inspections to ensure they are free of defects. Each day, they randomly select a sample of 200 pens. To do this, they randomly select one of the first 100 pens produced, and then they select every 100th pen produced after that. Each selected pen is then tested for quality. Is the resulting sample of 200 pens a simple random sample?

Question

14-03-2024
Mathematics

High School

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A production line in a large factory produces 20,000 ballpoint pens per day. The company performs quality control inspections to ensure they are free of defects. Each day, they randomly select a sample of 200 pens. To do this, they randomly select one of the first 100 pens produced, and then they select every 100th pen produced after that. Each selected pen is then tested for quality. Is the resulting sample of 200 pens a simple random sample?

Answer :

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NishaPr NishaPr · Answer 1 · 2024-11-09T05:28:16-05:00

Final answer:

The sample of 200 pens from the production line for quality testing is not a simple random sample because not every pen has an equal chance of being selected. The sampling method used is systematic, rather than random.

Explanation:

The 200 pens that are selected each day for testing on the production line in the large factory are not a simple random sample. A simple random sample is defined as a subset of a statistical population in which each member of the subset has an equal probability of being chosen.

In this scenario, however, the methodology used doesn't give every pen an equal chance of being selected. The first selection is made from the first 100 pens produced, and thereafter, every 100th pen is chosen. This implies that pens produced between these set intervals do not have a chance to be in the sample. Therefore, while the sample is systematic, it isn't a simple random sample.

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