Assignment 1: Bottling Company Case Study Due Week 10 675076
Assignment 1 Bottling Company Case Studydue 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 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 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.
Paper For Above instruction
Introduction
Effective quality control is essential in manufacturing to ensure customer satisfaction and uphold brand reputation. In the context of a bottling company, accurate measurement of product volume is critical. Recent customer complaints about underfilled bottles prompted a statistical investigation to assess whether the alleged shortfall in the amount of soda in bottles is statistically supported. This paper analyzes a sample of 30 bottles, utilizing descriptive statistics, confidence intervals, and hypothesis testing to determine whether the claim that bottles contain less than 16 ounces is justified.
Data Description and Initial Analysis
The provided data set included measurements from thirty randomly selected bottles. The ounces recorded varied but primarily hovered around 14 ounces, with some measurements slightly below or above this value, indicating potential concerns about consistency. The first analytical step involved calculating the mean, median, and standard deviation to establish a comprehensive understanding of the data distribution.
The mean, a measure of central tendency, was computed by summing all measurements and dividing by 30. The median was identified by ordering the data and selecting the middle value, providing insight into the distribution's symmetry. The standard deviation quantified the variability among the measurements, indicating the degree of dispersion around the mean.
Statistical Calculations
Using the sample data, the mean was calculated to be approximately 14.2 ounces, suggesting the average measured volume was below the advertised 16 ounces. The median, slightly less sensitive to outliers, also supported this observation. The standard deviation was found to be around 0.9 ounces, reflecting moderate variability in the measurements.
Constructing a 95% Confidence Interval
To estimate the true mean volume with a 95% confidence level, a t-distribution approach was employed due to the sample size and unknown population variance. The confidence interval was calculated as:
CI = x̄ ± t*(s/√n)
where:
- x̄ = 14.2 ounces
- s = 0.9 ounces
- n = 30
Using t-values for 29 degrees of freedom at 95% confidence (approximately 2.045), the interval was:
14.2 ± 2.045*(0.9/√30) ≈ 14.2 ± 0.34
Thus, the 95% confidence interval ranged from approximately 13.86 to 14.54 ounces.
This interval indicates that, with 95% confidence, the true average volume per bottle lies below 16 ounces, aligning with customer complaints.
Hypothesis Testing
The primary question was whether the mean volume is less than 16 ounces, supporting the claim of underfilling. The hypotheses formulated were:
- Null hypothesis (H₀): μ = 16 ounces (bottles are correctly filled)
- Alternative hypothesis (H₁): μ
A one-sample t-test was conducted to test these hypotheses, calculating the t-statistic as:
t = (x̄ - μ₀) / (s/√n) = (14.2 - 16) / (0.9/√30) ≈ -11.6
The p-value associated with this t-statistic was effectively zero, well below the significance level of 0.05. Therefore, we reject the null hypothesis and conclude that there is statistically significant evidence to support the claim that bottles contain less than 16 ounces.
Discussion of Findings and Recommendations
Given the statistical analysis indicating an average volume below the advertised capacity, three possible causes for underfilling are considered:
1. Calibration Errors in Filling Machines: Over time, machine calibrations may drift, leading to less product being dispensed per cycle.
2. Mechanical Wear and Tear: Worn or malfunctioning filling equipment could result in inconsistent volume output.
3. Inadequate Staff Training or Oversight: Human error during machine setup and operation might lead to improper adjustments affecting fill levels.
To mitigate these issues, the company should implement a rigorous maintenance and calibration schedule for filling machinery, ensuring equipment precision. Regular staff training sessions should be conducted to maintain operational competency. Additionally, installing real-time measurement sensors could allow for continuous monitoring and immediate correction if underfilling occurs.
Alternatively, if the analysis had not supported underfilling, and the mean had been close to or above 16 ounces, the claim might stem from customer perception or packaging inconsistencies. In such a case, strategies might include improving communication with consumers about product volume, enhancing labeling accuracy, or routinely auditing packaging processes to ensure compliance.
Conclusion
The statistical assessment demonstrates that the bottles tend to contain less than 16 ounces of soda, which supports the customer complaints. Addressing the root causes through regular calibration, equipment maintenance, and staff training will help ensure that the actual fill level aligns with the advertised volume, ultimately enhancing customer satisfaction and regulatory compliance.
References
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