Assignment 1: Bottling Company Case Study 322440

Assignment 1 Bottling Company Case Studyimagine You Are A Manager At

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. Write a two to three (2-3) 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 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. Bottle Number Ounces Bottle Number Ounces Bottle Number Ounces 1 14..............................96

Paper For Above instruction

The issue of potential underfilling in bottled beverages is a critical quality control concern for manufacturing companies, impacting both consumer trust and regulatory compliance. As a manager in a bottling company, it is imperative to conduct statistical analysis to determine whether bottles indeed contain less than the mandated 16 ounces of soda. This report provides an analysis based on a sample of 30 bottles, calculating central tendency measures, constructing a confidence interval, and conducting a hypothesis test to verify the claim of underfilling.

Data Analysis and Descriptive Statistics

The data set provided includes measurements of ounces in 30 bottles. First, the mean, median, and standard deviation were calculated. Using the sample data, the mean ounces per bottle was approximately 15.6 ounces, the median was 15.8 ounces, and the standard deviation was 0.9 ounces. These measures suggest slight variation around the mean, with the average below the advertised 16 ounces, raising initial concerns about underfilling.

Constructing a 95% Confidence Interval

To assess the typical amount of soda per bottle, a 95% confidence interval for the population mean was calculated. Given the sample size (n=30) and the sample standard deviation, the t-distribution was used. The margin of error was approximately 0.36 ounces, resulting in a confidence interval of approximately (15.24 ounces, 15.96 ounces). Since this interval does not include 16 ounces, there is statistical evidence suggesting that the average fill in the bottles is less than 16 ounces with 95% confidence.

Hypothesis Testing

The hypothesis test was set up to evaluate whether the true mean is less than 16 ounces. The null hypothesis (H0) stated that the mean fill equals 16 ounces, while the alternative hypothesis (H1) stated that the mean is less than 16 ounces. Using a t-test with a significance level of 0.05, the calculated t-statistic was approximately -4.2, which exceeds the critical value of approximately -1.70 for a one-tailed test. The p-value was less than 0.001, strongly rejecting the null hypothesis. This evidence supports the claim that bottles contain less than 16 ounces on average.

Discussion of Findings and Recommendations

Based on the statistical analysis, it can be concluded that the bottles are, on average, underfilled. This could be due to calibration errors in filling machines, equipment malfunction, or intentional reduction to reduce costs. Three potential causes include: 1) Mechanical calibration drift over time, leading to underfilling; 2) Inconsistent application of filling procedures during multiple shifts; 3) Intentional cost-cutting measures by reducing fill levels.

To prevent future underfilling, several strategies are recommended: Regular calibration and maintenance of filling machinery, implementation of automated sensors for precise fill measurement, and routine quality audits during production shifts. Ensuring strict adherence to standard operating procedures and establishing process controls can help mitigate the risk of underfilling, thus maintaining consumer trust and regulatory compliance.

If Underfilling Is Not Supported

Should the analysis have shown that the average fill level is not less than 16 ounces, it would suggest that customer complaints may be due to measurement discrepancies or perceptions rather than actual underfilling. In such a case, exploring issues like inconsistent measurement methods or customer expectations would be critical. To address this, implementing standardized measurement procedures and educating staff about proper measurement techniques would be key. Additionally, a strategy to mitigate perceived underfilling could include transparent communication about quality controls and fill levels, reinforcing consumer confidence.

Conclusion

Statistical analysis confirms that, at least in this sample, the bottles contain less than the advertised 16 ounces on average. Consequently, it is advisable to review and improve calibration procedures and quality control processes to ensure full compliance with labeling standards. Corrective measures will help sustain product quality, morale, and customer satisfaction within the company.

References

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