To determine the percentage of defective light bulbs in the production line, the sampling method chosen should be representative of the entire production line to ensure valid inference. Let's evaluate the options:
a. Test every 50th light bulb in the production line: This method is a systematic sampling approach. Assuming that the production line is homogeneous, this method is likely to provide a representative sample and can lead to valid inferences about the entire population.
b. Testing the last 4,000 bulbs in the production line: Testing only the last part of the production may introduce bias, as the quality of bulbs could change over time during production. This might not be representative of the entire production lot.
c. Testing the first 2,000 light bulbs in the production line: Similar to option b, testing only the first part of the production may not represent the overall quality, especially if there are changes in manufacturing processes that occur over time.
d. Retesting 100 light bulbs that have already been tested: Retesting the same bulbs does not provide new information about the overall production, so this method is not effective for inferring the percentage of defects in the entire production line.
Given these evaluations, the best choice for valid inference is:
a. Test every 50th light bulb in the production line.