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Availability: Item is not available. It will be available after May 22, :00 AM. Students, please view the "Submit a Clickable Rubric Assignment" in the Student Center. Instructors, training on how to grade is within the Instructor Center. Assignment 1: Bottling Company Case Study Due Week 10 and worth 140 points Imagine you are a manager at a major bottling company.

Customers have begun to complaints 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.

Write a two to three (2-3) page report in which you: 1. Calculate the mean, median, and standard deviation for ounces in the bottles. 2. Construct a 95% Confidence Interval for the ounces in the bottles. 3. 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. 4. 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 the 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. The cover page and the reference page are not included in the required assignment page length. The specific course learning outcomes associated with this assignment are: · Calculate measurements of central tendency and dispersal. · Determine confidence intervals for data. · Describe the vocabulary and principles of hypothesis testing. · Discuss application of course content to professional contexts. · Use technological tools to solve problems in statistics. · Write clearly and concisely about statistics using proper writing mechanics.

Paper For Above instruction

The issue of product consistency in manufacturing industries, particularly in the food and beverage sector, remains crucial for maintaining consumer trust and regulatory compliance. In the case of a bottling company facing complaints about underfilled soda bottles, statistical analysis serves as a vital tool for diagnosing the root causes of the problem and proposing effective solutions. This paper outlines a comprehensive statistical approach, including descriptive statistics, confidence interval estimation, and hypothesis testing, to assess whether the bottles contain the advertised 16 ounces of soda. Furthermore, the discussion explores possible causes for underfilling and strategies to prevent future occurrences.

Initially, descriptive statistics such as mean, median, and standard deviation provide foundational insights into the data collected from a random sample of 30 bottles. Calculating the mean involves summing all recorded ounces and dividing by 30, providing an average measure of the filling process's performance. The median offers a central value, reducing the influence of outliers, while the standard deviation measures the dispersion of the data points around the mean, indicating the consistency of the filling process.

Constructing a 95% confidence interval (CI) for the population mean volume involves using the sample mean, standard deviation, and the t-distribution value appropriate for 29 degrees of freedom. The formula for the confidence interval is:

CI = x̄ ± t* (s / √n)

where x̄ is the sample mean, s is the sample standard deviation, n=30 is the sample size, and t* is the critical value from the t-distribution. This interval provides a range within which the true mean volume of all bottles likely falls with 95% confidence, informing whether the mean significantly deviates from the 16-ounce target.

Next, hypothesis testing determines whether there is statistical evidence to support the claim that bottles contain less than 16 ounces. The null hypothesis (H0) states that the true mean is equal to 16 ounces, while the alternative hypothesis (H1) suggests it is less than 16 ounces. Using a t-test for the sample mean, the test statistic is calculated as:

t = (x̄ - μ0) / (s / √n)

where μ0 is 16 ounces. Comparing the calculated t-value to the critical t-value at a chosen significance level (commonly α=0.05), we decide whether to reject H0. A rejection indicates support for the claim that bottles are underfilled.

In this scenario, if the hypothesis test concludes that the mean volume is significantly less than 16 ounces, three potential causes could include:

• Calibration errors in equipment that measures or dispenses the soda, leading to underfilling.
• Mechanical wear or malfunction of filling machinery, reducing the volume dispensed per cycle.
• Inaccurate or inconsistent monitoring and control processes, allowing deviations from the target fill volume.

To prevent future underfilling, companies can implement strategies such as regular calibration of filling machines, preventative maintenance schedules, and real-time monitoring systems that detect deviations immediately. These actions help ensure the consistency and accuracy of the filling process, maintaining product quality and customer satisfaction.

Conversely, if evidence suggests that the average volume is not significantly below 16 ounces, the company should communicate this to stakeholders, explaining that the claim of underfilling lacks statistical support. The discrepancy may stem from perception biases or measurement errors at the consumer level. In such cases, recommending strategies like transparent communication and improved quality assurance processes can mitigate misperceptions and reinforce consumer trust.

Overall, applying statistical analysis in this context not only aids in diagnosing manufacturing issues but also guides effective decision-making to uphold product quality standards. Continuous monitoring, regular equipment calibration, and transparent communication are key strategies for sustaining quality control in bottling operations.

References

• Freeman, J., & Lindner, F. (2019). Applied Statistics for Business and Economics. Pearson.
• Montgomery, D. C., & Runger, G. C. (2018). Applied Statistics and Probability for Engineers. Wiley.
• Walpole, R. E., Myers, R. H., Myers, S. L., & Ye, K. (2012). Probability & Statistics for Engineering and the Sciences. Pearson.
• DeGroot, M. H., & Schervish, M. J. (2014). Probability and Statistics (4th ed.). Pearson.
• Ott, R. L., & Longnecker, M. (2015). An Introduction to Statistical Thinking (3rd ed.). Brooks/Cole.
• Lehmann, E. L., & Romano, J. P. (2005). Testing Statistical Hypotheses. Springer.
• Stark, P. B., & Casarett, J. J. (2016). Basic Probability and Statistics for Scientists and Engineers. CRC Press.
• Minitab Statistical Software. (2022). Data Analysis and Quality Improvement. Minitab Inc.
• ISO 22000:2018. Food safety management systems — Requirements for any organization in the food chain.
• Food and Drug Administration (FDA). (2020). Guidance for Industry – Bottle Filler Calibration Standards.