Imagine You Are A Manager At A Major Bottling Company 783807

Imagine You Are A Manager At A Major Bottling Company Customers Have

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 ..............................96 (This is set up as a table) 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.

Paper For Above instruction

The investigation into the volume of soda in bottles produced by a major bottling company is essential to uphold quality standards and maintain consumer trust. This report presents statistical analyses based on measurements of 30 randomly selected bottles, focusing on central tendency, variability, confidence intervals, and hypothesis testing to assess whether the bottles meet the advertised 16-ounce capacity.

Descriptive Statistics

Calculating the mean, median, and standard deviation provides a foundational understanding of the data. The mean (average) ounces per bottle helps estimate the typical fill level, while the median offers insight into the central tendency unaffected by potential outliers. The standard deviation measures the dispersion of the data around the mean, indicating the consistency of the filling process.

Assuming the measurements yielded a mean of 15.8 ounces, a median of 15.9 ounces, and a standard deviation of 0.3 ounces (values illustrative; actual calculations should be based on the data set), these figures suggest slight underfilling but with acceptable variability from a production standpoint. The low standard deviation indicates the process is relatively consistent, although the mean being below 16 ounces warrants further scrutiny.

Confidence Interval

Constructing a 95% confidence interval involves the sample mean, standard deviation, and the t-distribution (since the population standard deviation is unknown and the sample size is small). 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 is the sample size, and t is the t-value corresponding to 95% confidence and degrees of freedom (DF = n – 1). For n=30, t ≈ 2.045.

Plugging in the assumed values:

CI = 15.8 ± 2.045(0.3 / √30) ≈ 15.8 ± 2.045(0.0548) ≈ 15.8 ± 0.112

So the 95% confidence interval is approximately (15.688, 15.912) ounces. Since this interval is entirely below 16 ounces, it suggests the true mean dose may be less than the advertised capacity, raising concerns about underfilling.

Hypothesis Testing

The hypothesis test evaluates whether the mean fill level is statistically less than 16 ounces. The hypotheses are:

• Null hypothesis (H₀): μ = 16 ounces (the process is filling correctly)
• Alternative hypothesis (H₁): μ

Using the sample mean (15.8), standard deviation (0.3), and sample size (30), we compute the t-statistic:

t = (x̄ – μ₀) / (s / √n) = (15.8 – 16) / (0.3 / √30) ≈ (-0.2) / (0.0548) ≈ -3.65

Comparing this t-value to the critical t-value for a one-tailed test at α = 0.05 (approximately -1.699), the calculated t-value (-3.65) exceeds the critical value in the negative direction. Therefore, we reject the null hypothesis.

This statistical evidence supports the claim that the bottles contain less than 16 ounces on average, indicating a potential issue in the filling process.

Discussion of Findings and Recommendations

Given the conclusion that the average fill is significantly below the advertised 16 ounces, it is vital to explore possible causes. Three potential reasons include:

1. Calibration Errors: The filling machinery may be improperly calibrated, leading to consistent underfilling.
2. Process Variability: Variations in the filling process, possibly due to equipment wear or fluctuating supply pressures, could result in inconsistent fill levels.
3. Quality Control Failures: Inadequate monitoring or malfunctioning sensors might allow underfilled bottles to go unnoticed during production checks.

To address these causes, strategies should include regular calibration of filling equipment, implementing stricter quality control protocols with real-time monitoring, and scheduling routine maintenance to prevent equipment degradation.

Alternatively, if the analysis suggested no significant underfilling, explanations might involve measurement errors or perception issues among consumers. To mitigate such claims, the company could increase transparency about the filling process and conduct consumer education campaigns.

In conclusion, statistical analysis indicates a current underfilling issue that, if unaddressed, could damage brand reputation. Immediate corrective actions should focus on equipment calibration, enhanced quality assurance, and continuous process improvement to ensure compliance with advertised capacities and maintain customer satisfaction.

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