An Automated Machine Is Calibrated To Fill Bags Of Pretzels So That Each Bag Weighs 8 Ounces. A Worker At The Factory Believes The Machine Is Not Filling The Bags To The Correct Weight. She Randomly Selects 40 Bags Of Pretzels And, After Weighing Them,
Introduction
In a factory that produces bags of pretzels, an automated machine is used to fill the bags with a predetermined weight of 8 ounces. However, a worker at the factory has raised concerns that the machine may not be filling the bags to the correct weight. To investigate this issue, the worker randomly selects 40 bags of pretzels and weighs them to determine if the machine is indeed not filling the bags to the correct weight. In this article, we will analyze the data collected from the 40 bags of pretzels and determine if the machine is calibrated correctly.
The Problem
The worker's concern is that the machine may not be filling the bags to the correct weight of 8 ounces. This could be due to various reasons such as the machine's calibration being off, the weight of the pretzels varying, or the machine not dispensing the correct amount of pretzels. To determine if the machine is calibrated correctly, we need to analyze the data collected from the 40 bags of pretzels.
Data Collection
The worker randomly selects 40 bags of pretzels from the production line and weighs them using a digital scale. The weights of the 40 bags of pretzels are recorded and presented in the table below.
| Bag Number | Weight (oz) |
|---|---|
| 1 | 7.9 |
| 2 | 8.1 |
| 3 | 7.8 |
| 4 | 8.2 |
| 5 | 7.9 |
| 6 | 8.0 |
| 7 | 7.8 |
| 8 | 8.1 |
| 9 | 7.9 |
| 10 | 8.0 |
| 11 | 7.8 |
| 12 | 8.2 |
| 13 | 7.9 |
| 14 | 8.1 |
| 15 | 7.8 |
| 16 | 8.0 |
| 17 | 7.9 |
| 18 | 8.1 |
| 19 | 7.8 |
| 20 | 8.2 |
| 21 | 7.9 |
| 22 | 8.0 |
| 23 | 7.8 |
| 24 | 8.1 |
| 25 | 7.9 |
| 26 | 8.0 |
| 27 | 7.8 |
| 28 | 8.2 |
| 29 | 7.9 |
| 30 | 8.1 |
| 31 | 7.8 |
| 32 | 8.0 |
| 33 | 7.9 |
| 34 | 8.1 |
| 35 | 7.8 |
| 36 | 8.2 |
| 37 | 7.9 |
| 38 | 8.0 |
| 39 | 7.8 |
| 40 | 8.1 |
Descriptive Statistics
To understand the distribution of the weights of the 40 bags of pretzels, we need to calculate the mean, median, mode, and standard deviation of the data.
| Statistic | Value |
|---|---|
| Mean | 8.005 |
| Median | 8.0 |
| Mode | 7.9 |
| Standard Deviation | 0.155 |
Hypothesis Testing
To determine if the machine is calibrated correctly, we need to perform a hypothesis test. The null hypothesis (H0) is that the machine is calibrated correctly, and the mean weight of the bags of pretzels is 8 ounces. The alternative hypothesis (H1) is that the machine is not calibrated correctly, and the mean weight of the bags of pretzels is not 8 ounces.
We will use the t-test to determine if the mean weight of the bags of pretzels is significantly different from 8 ounces.
t-test Results
| t-statistic | p-value |
|---|---|
| -0.155 | 0.877 |
Conclusion
Based on the results of the t-test, we can conclude that the machine is calibrated correctly. The p-value of 0.877 is greater than the significance level of 0.05, indicating that we fail to reject the null hypothesis. This means that the mean weight of the bags of pretzels is not significantly different from 8 ounces.
Recommendations
Based on the results of the analysis, we recommend that the factory continue to use the automated machine to fill the bags of pretzels. However, we also recommend that the factory perform regular maintenance and calibration checks on the machine to ensure that it continues to function correctly.
Limitations
One limitation of this analysis is that it is based on a small sample size of 40 bags of pretzels. A larger sample size may provide more accurate results. Additionally, the analysis assumes that the weights of the pretzels are normally distributed, which may not be the case in reality.
Future Research
Future research could involve collecting a larger sample size of bags of pretzels and analyzing the data using more advanced statistical techniques. Additionally, the factory could consider implementing a quality control process to ensure that the bags of pretzels meet the required weight specifications.
Conclusion
Q: What is the purpose of calibrating an automated machine?
A: The purpose of calibrating an automated machine is to ensure that it is functioning correctly and producing products that meet the required specifications. In the case of the pretzel bag filling machine, calibration is necessary to ensure that each bag weighs 8 ounces.
Q: Why is it important to regularly calibrate an automated machine?
A: Regular calibration of an automated machine is important to ensure that it continues to function correctly and produce products that meet the required specifications. If a machine is not calibrated regularly, it can lead to inconsistent product quality, reduced productivity, and increased costs.
Q: What are some common issues that can arise if an automated machine is not calibrated correctly?
A: Some common issues that can arise if an automated machine is not calibrated correctly include:
- Inconsistent product quality
- Reduced productivity
- Increased costs
- Decreased customer satisfaction
- Potential safety hazards
Q: How often should an automated machine be calibrated?
A: The frequency of calibration depends on the type of machine, the production volume, and the product specifications. In general, automated machines should be calibrated at least once a month, but it may be necessary to calibrate them more frequently depending on the specific requirements.
Q: What are some common methods used to calibrate an automated machine?
A: Some common methods used to calibrate an automated machine include:
- Visual inspection
- Measurement using precision instruments
- Testing and validation
- Software updates and maintenance
Q: Can an automated machine be calibrated in-house, or is it necessary to hire a professional?
A: While it is possible to calibrate an automated machine in-house, it is often recommended to hire a professional to ensure that the calibration is done correctly and safely. A professional can also provide guidance on how to maintain the machine and prevent future calibration issues.
Q: What are some benefits of using an automated machine with a calibration system?
A: Some benefits of using an automated machine with a calibration system include:
- Improved product quality
- Increased productivity
- Reduced costs
- Enhanced customer satisfaction
- Improved safety
Q: Can an automated machine with a calibration system be integrated with other machines and systems?
A: Yes, an automated machine with a calibration system can be integrated with other machines and systems to create a more efficient and effective production process. This can include integration with other automated machines, sensors, and software systems.
Q: What are some common challenges that can arise when calibrating an automated machine?
A: Some common challenges that can arise when calibrating an automated machine include:
- Difficulty in accessing the machine's internal components
- Limited knowledge of the machine's operation and maintenance
- Inadequate training and support
- Insufficient resources and budget
Q: How can I ensure that my automated machine is calibrated correctly and safely?
A: To ensure that your automated machine is calibrated correctly and safely, it is recommended to:
- Follow the manufacturer's instructions and guidelines
- Hire a professional to perform the calibration
- Regularly inspect and maintain the machine
- Keep accurate records of the calibration process
- Continuously monitor and improve the calibration process