To determine the percentage of defective light bulbs in a production line, the sampling method should be representative of the whole population of light bulbs produced. Let's analyze each option:
A) Testing every fiftieth light bulb in the production line - This method is systematic sampling. If the manufacturing process is consistent and random, this could provide a good representation of the entire batch.
B) Testing the first 2,000 light bulbs in the production line - This method might introduce bias because the first 2,000 bulbs may not represent the entire production run, especially if production quality changes over time.
C) Testing the last 4,000 bulbs in the production line - Similar to option B, this could also be biased as the quality of the last bulbs may differ from earlier batches, especially if there are issues that arise toward the end of the production run.
D) Retesting 100 light bulbs that have already been tested - This does not provide any new information about the overall defect rate since it is testing the same bulbs again.
Based on this analysis, the best option is:
A) Testing every fiftieth light bulb in the production line.
This method is most likely to lead to a valid inference about the overall percentage of defective light bulbs.