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?
A- testing the first 2,000 light bulbs in the production line
B- testing every fiftieth light bulb in the production line
C- retesting 100 light bulbs that have already been tested
D -testing the last 4,000 bulbs in the production line
B- testing every fiftieth light bulb in the production line. This is a form of systematic sampling, where every Nth item is selected for testing. It ensures that the sample is representative of the population and reduces the likelihood of bias or non-representativeness. The other sampling methods may introduce biases or may not be representative of the entire production line.
Avery randomly selects 50 colored pencils from a basket and finds that 2 are not sharpened. If the basket contains 300 colored pencils, how many would you expect to be unsharpened?
A 20
B 120
C 2
D 12
The sampling method that would most likely lead to a valid inference is option B - testing every fiftieth light bulb in the production line.
This method ensures a random and representative selection of light bulbs from the entire production line, which is crucial for obtaining accurate information about the percentage of defective light bulbs. Testing the first 2,000 bulbs (option A) or the last 4,000 bulbs (option D) may not provide a representative sample if there are potential variations or trends throughout the production process. Retesting 100 bulbs that have already been tested (option C) also does not ensure a random and representative sample.
To determine the percentage of defective light bulbs in the production line, the quality control manager needs to employ a sampling method that will lead to a valid inference. Let's evaluate each option:
A- Testing the first 2,000 light bulbs: This option may introduce bias because the first 2,000 light bulbs may not be representative of the entire production line. It is possible that there could be some variations or issues with the initial batches that differ from the rest of the production. Therefore, this sampling method may not lead to a valid inference.
B- Testing every fiftieth light bulb: Sampling every fiftieth light bulb could introduce bias if there is a regular or cyclical pattern in the production line that may inadvertently include or exclude certain defective light bulbs. This may not lead to a representative sample, and the inference may not be valid.
C- Retesting 100 light bulbs that have already been tested: This sampling method would not provide additional information about the percentage of defective light bulbs if the same 100 light bulbs are retested. It would be like counting the same light bulbs twice, and the inference would not be valid.
D- Testing the last 4,000 bulbs: This option may be a valid sampling method because it covers a significant portion of the production line. If the production process is consistent and there is no substantial variation throughout the production line, testing the last 4,000 bulbs could provide a representative sample that leads to a valid inference.
Based on the analysis, option D - testing the last 4,000 bulbs in the production line - would most likely lead to a valid inference regarding the percentage of defective light bulbs.