A quality control manager wants to determine the percentage of defective light bulbs in the production line. Which of the following sampling methods would most likely lead to a valid inference?
testing the first 2,000 light bulbs in the production line
retesting 100 light bulbs that have already been tested
testing the last 4,000 bulbs in the production line
testing every fiftieth light bulb in the production line
Testing every fiftieth light bulb in the production line would most likely lead to a valid inference as it is a form of systematic random sampling. It ensures that every part of the production line has an equal opportunity to be represented in the sample, reducing the risk of bias and providing a representative sample. The other methods may be biased towards certain parts of the production line or may not be representative of the entire batch.
The sampling method that would most likely lead to a valid inference in this case is testing every fiftieth light bulb in the production line.
When it comes to quality control, it is important to have a representative and unbiased sample. Each method listed has its own advantages and drawbacks, but testing every fiftieth light bulb in the production line would likely provide the best representation of the overall quality. By sampling every fiftieth bulb, you would cover a broader range of bulbs and minimize the chance of bias compared to the other options.
Testing the first 2,000 light bulbs may introduce bias if the production process and quality control measures have improved or changed over time. Retesting 100 light bulbs that have already been tested may not provide an accurate representation of the overall quality if the initial sample was not representative. Testing the last 4,000 bulbs may not be representative of the entire production line if there are variations in the process that could affect quality.
Testing every fiftieth light bulb would allow for a more systematic and unbiased sample, ensuring a better estimation of the overall percentage of defective light bulbs in the production line.