A production line operation is designed to fill cartons with laundry detergent to a mean weight of 32 ounces. A sample of cartons is periodically selected and weighed to determine whether underfilling or overfilling is occurring. If the sample data lead to a conclusion of underfilling or overfilling, the production line will be shut down and adjusted to obtain proper filling.
What is your question?
To determine whether underfilling or overfilling is occurring in the production line, you need to analyze the sample data obtained from periodically selected cartons. Here's how you can approach the analysis:
1. Collect the sample data: Select a random sample of cartons from the production line periodically. The sample size should be large enough to provide a representative picture of the overall filling process.
2. Weigh the cartons: Measure the weight of each carton in the sample using a reliable weighing scale. Record these measurements.
3. Calculate the sample mean: Add up all the recorded weights and divide the sum by the number of cartons in the sample to calculate the sample mean.
4. Compare the sample mean to the target weight: In this case, the target weight is 32 ounces. Compare the sample mean obtained in the previous step to the target weight to see if it falls within an acceptable range.
- If the sample mean is close to 32 ounces, you can conclude that the production line is generally filling the cartons properly.
- If the sample mean is consistently below 32 ounces, the production line may be underfilling the cartons.
- If the sample mean is consistently above 32 ounces, the production line may be overfilling the cartons.
5. Determine statistical significance: To obtain a more rigorous conclusion, you can perform a statistical analysis. Calculate the sample standard deviation, and then use a statistical hypothesis test, such as a one-sample t-test or a z-test, to determine whether the difference between the sample mean and the target weight is statistically significant.
- If the difference is statistically significant, it indicates a systematic issue with underfilling or overfilling that requires adjustment.
- If the difference is not statistically significant, it suggests that any deviations from the target weight are likely due to random variation inherent in the production process.
6. Take action: If the data analysis leads to a conclusion of underfilling or overfilling, it's important to shut down the production line and make necessary adjustments to ensure proper filling. This may involve recalibrating the filling system or making changes to the production process.
By following these steps and analyzing the sample data, you can accurately determine whether underfilling or overfilling is occurring in the production line and take appropriate actions to maintain the desired filling levels.