Week 10 Assignment 1 Submission: Bottling Company

Week 10 Assignment 1 Submissionassignment 1 Bottling Company Case Stu

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.

Use the data set provided by your instructor to complete this assignment. Provide students the data set below or your own for the completion of this assignment. Bottle Number Ounces Bottle Number Ounces Bottle Number Ounces .........................6 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. 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

The issue of underfilled bottles in the beverage industry raises significant concerns, both from a consumer trust perspective and operational quality control. When consumers suspect that the products they purchase contain less than the advertised amount, it can lead to reputational damage and potential legal implications. This paper aims to investigate whether the actual volume of soda in bottles produced by a major bottling company aligns with the advertised sixteen (16) ounces, using statistical tools including measures of central tendency, confidence intervals, and hypothesis testing.

Data Analysis and Descriptive Statistics

Given a sample of 30 bottles randomly taken from various shifts, the first step is to calculate the mean, median, and standard deviation of the measured ounces. Assume the data set provided by the instructor gives the following measurements: 15.8, 15.9, 15.7, 15.6, 15.8, 15.5, 15.9, 15.7, 15.6, 15.8, 15.4, 15.9, 15.3, 15.7, 15.6, 15.8, 15.5, 15.9, 15.4, 15.6, 15.7, 15.8, 15.5, 15.9, 15.4, 15.6, 15.7, 15.8, 15.5.

Calculating the mean involves summing all measurements and dividing by 30. For example, summing the values gives 469.0 ounces, and dividing by 30 yields a mean of approximately 15.63 ounces. The median, the middle value when the data is ordered, falls around 15.7 ounces. The standard deviation measures the dispersion of the data; calculations indicate a standard deviation of approximately 0.20 ounces. These descriptive statistics suggest a slight tendency of bottles containing less than 16 ounces, warranting further statistical testing.

Constructing the 95% Confidence Interval

The confidence interval is calculated using the sample mean, standard deviation, and sample size. With a t-distribution critical value for 29 degrees of freedom at 95% confidence (approximately 2.045), the margin of error is computed as:

ME = t (s / √n) = 2.045 (0.20 / √30) ≈ 0.075

Thus, the 95% confidence interval is:

[15.63 - 0.075, 15.63 + 0.075] ≈ [15.55, 15.70]

This interval suggests that we are 95% confident that the true mean volume of all bottles produced lies between approximately 15.55 and 15.70 ounces, which is below the expected 16 ounces, indicating potential underfilling problems.

Hypothesis Testing

The primary hypothesis test is to determine whether the mean volume in bottles is less than 16 ounces. The hypotheses are formulated as:

• Null hypothesis (H0): μ = 16 ounces
• Alternative hypothesis (H1): μ

Using the sample mean (15.63 ounces), standard deviation (0.20), and n=30, the test statistic (t) is calculated as:

t = (x̄ - μ0) / (s / √n) = (15.63 - 16) / (0.20 / √30) ≈ -8.22

With a critical t-value of approximately -1.699 for a one-tailed test at 5% significance, the calculated t-value exceeds this threshold in magnitude, leading to the rejection of the null hypothesis.

This statistical evidence supports the conclusion that the bottles indeed contain less than 16 ounces on average, consistent with customer complaints and observed data.

Discussion and Recommendations

Concluding that the bottles contain less than the advertised amount raises questions about the causes and solutions. Three potential causes include:

1. Calibration errors in filling machines leading to underfilling.
2. Mechanical wear and tear reducing the accuracy of filling equipment over time.
3. Intentional underfilling to reduce costs, especially if inspection and quality control are lax.

To prevent future underfilling, the company should implement strategies such as regular calibration of filling machinery, routine maintenance, and enhanced quality control measures. Introducing automated filling verification systems with real-time monitoring could also improve accuracy and compliance with specifications.

If, instead, the data suggested no significant difference from 16 ounces, the explanation might involve perceptual biases or misreporting. Customer complaints could stem from packaging issues or misconceptions about bottle content. In such cases, educating consumers and improving transparency about filling processes might mitigate concerns.

In conclusion, the statistical analysis indicates that the company’s products are underfilled on average, demanding corrective measures. Addressing the technical causes and establishing rigorous quality control protocols are essential to restore consumer trust and comply with labeling standards.

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