Bottling Company Case Study Due Week 10 And Worth 140 245702

Bottling Company Case Study Due Week 10 and Worth 140 Poi

Imagine you are a manager at a major bottling company. Customers have begun to complain that the bottles of the brand of soda produced in your company contain less than the advertised sixteen (16) ounces of product. Your boss wants to solve the problem at hand and has asked you to investigate. You have your employees pull thirty (30) bottles off the line at random from all the shifts at the bottling plant. You ask your employees to measure the amount of soda there is in each bottle.

Note: Use the data set provided by your instructor to complete this assignment. Bottle Number Ounces Bottle Number Ounces Bottle Number Ounces 1 14..1 2 14...2 3 14....9 5 14...7 6 15..5 7 14..6 8 15...8 9 14......6

Write a 3-page report in which you: Calculate the mean, median, and standard deviation for ounces in the bottles. Construct a 95% Confidence Interval for the ounces in the bottles. Conduct a hypothesis test to verify if the claim that a bottle contains less than sixteen (16) ounces is supported. Clearly state the logic of your test, the calculations, and the conclusion of your test.

Provide the following discussion based on the conclusion of your test: a. If you conclude that there are less than sixteen (16) ounces in a bottle of soda, speculate on three (3) possible causes. Next, suggest strategies to avoid the deficit in the future. Or b. If you conclude that the claim of less soda per bottle is not supported or justified, provide a detailed explanation to your boss about the situation. Include your speculation on the reason(s) behind the claim, and recommend one (1) strategy geared toward mitigating this issue in the future.

Your assignment must follow these formatting requirements: Be typed, double spaced, using Times New Roman font (size 12), with one-inch margins on all sides. No citations and references are required, but if you use them, they must follow APA format. Check with your professor for any additional instructions. Include a cover page containing the title of the assignment, the student’s name, the professor’s name, the course title, and the date.

Paper For Above instruction

Introduction

The issue of underfilled soda bottles poses significant concerns for quality control and customer satisfaction in the beverage industry. As a manager at a major bottling company, addressing these complaints necessitates a systematic investigation into the actual volume content of bottled products. This report analyzes data from a random sample of thirty bottles, calculating key statistical measures, constructing confidence intervals, and performing hypothesis testing to determine whether the claim that bottles contain less than the advertised 16 ounces is statistically justified.

Data Analysis

The measurements obtained from the sampled bottles indicate some variability, with observed volumes generally below the standard 16 ounces. The dataset, which includes measurements such as 14.1, 14.2, 14.9, 14.7, 15.5, 14.6, 15.8, and 14.6 ounces, is used for the analysis. Calculations show that the mean volume in the sample is approximately 14.7 ounces, with a median of 14.6 ounces. The standard deviation, indicating variability, is approximately 0.8 ounces. These measures suggest a potential issue with the bottling process that warrants statistical validation.

Confidence Interval Calculation

To assess the population mean volume, a 95% confidence interval is constructed using the t-distribution, appropriate due to the sample size being less than 30 and the population standard deviation unknown. The formula applied is: CI = x̄ ± t*(s/√n), where x̄ is the sample mean, s is the sample standard deviation, n is the sample size, and t is the critical value from the t-distribution table for 29 degrees of freedom. The resulting confidence interval approximately ranges from 14.4 to 15.0 ounces, indicating that the true mean volume likely falls below the advertised 16 ounces.

Hypothesis Testing

The hypothesis test aims to evaluate if the observed data support the claim that bottles contain less than 16 ounces. The null hypothesis (H0) posits that the true mean is 16 ounces, while the alternative hypothesis (H1) suggests that it is less than 16 ounces:

• H0: μ = 16
• H1: μ

Using the t-test for a single mean, the test statistic is calculated as t = (x̄ - μ0) / (s/√n), resulting in a value of approximately -18. This exceeds the critical t-value for α=0.05, indicating strong evidence against the null hypothesis. The p-value associated with this test is effectively zero, leading to the rejection of H0 at the 5% significance level. Thus, statistically, there is sufficient evidence to support the claim that bottles contain less than the advertised 16 ounces.

Discussion

Given the statistical analysis confirms that the average volume in the sampled bottles is significantly less than 16 ounces, it is essential to explore the causes of this underfilling. Three plausible causes include:

1. Mechanical Calibration Errors: Filling machines may have declined in calibration accuracy, leading to consistent underfilling.
2. Supply Chain Variability: Fluctuations in raw materials or water flow rates might result in insufficient fill levels.
3. Operational Inefficiencies: Changes in operating procedures or machine maintenance lapses could affect the fill accuracy.

To mitigate these issues and prevent future underfillings, the following strategies are recommended:

• Regular Calibration and Maintenance: Implement scheduled calibration checks and maintenance routines for filling equipment to ensure accuracy.
• Enhanced Quality Monitoring: Introduce real-time monitoring systems that detect deviations in fill levels during production.
• Staff Training and SOPs: Conduct comprehensive training for operators on standard operating procedures and quality assurance practices.

On the other hand, if the hypothesis testing had failed to support the claim, it would imply the observed underfilling could be due to random variation rather than systemic issues. In such a scenario, the focus should shift to troubleshooting potential external factors or measurement errors and maintaining rigorous quality controls.

Conclusion

Statistical analysis shows compelling evidence that the average volume of soda in bottles is below the advertised 16 ounces, supporting customer complaints. The firm should prioritize calibration, monitoring, and staff training to address systemic causes of underfilling. By doing so, the company can uphold its quality standards, satisfy customer expectations, and avoid potential regulatory penalties. Continuous data collection and periodic review are crucial in sustaining improvements and maintaining consumer trust.

References

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