To determine the percentage of defective light bulbs in a production line, the sampling method should ideally provide a representative sample of the entire population of light bulbs. Among the options provided, the method that would most likely lead to a valid inference is:
Testing every fiftieth light bulb in the production line.
This method is considered a systematic sampling approach, which helps ensure that the sample is spread out evenly across the entire production batch. It reduces the risk of bias that might occur if only the first or last few bulbs were tested, and it avoids the issue of retesting bulbs that have already been evaluated.
The other methods have limitations:
- Testing the first 2,000 light bulbs could introduce bias because it may not account for variations that occur later in the production cycle.
- Retesting 100 light bulbs that have already been tested does not provide new information about other bulbs and could lead to a confirmation bias.
- Testing the last 4,000 bulbs may also introduce bias, similar to testing the first 2,000 bulbs, since production quality may vary over time.
Therefore, testing every fiftieth light bulb is the best choice for achieving a valid inference about the defect rate in the entire production line.