Bottling Company Case Study: Investigating Bottle Volume

Bottling Company Case Study: Investigating Bottle Volume Claims

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...96 Write a two to three (2-3) page report in which you:

Paper For Above instruction

Introduction

In the beverage industry, ensuring that bottles contain the right amount of product is crucial for customer satisfaction, regulatory compliance, and company reputation. Recently, customer complaints have indicated that some bottles contain less than the stated 16 ounces of soda, prompting an investigation into this issue. This study analyzes a sample of 30 bottles randomly selected from production, employing descriptive statistics and hypothesis testing to determine whether the bottles are indeed underfilled and to explore potential causes and solutions.

Descriptive Statistical Analysis

The first step involves calculating measures of central tendency and dispersion. The sample data comprises the measured ounces in each of the 30 sampled bottles. The mean provides an average measurement, indicating the typical amount of soda per bottle. The median offers the midpoint value, helping to understand the data distribution, especially if it’s skewed. The standard deviation quantifies the variability in the measurements, offering insights into consistency across bottles.

Assuming the sample data reveals, for example, a mean of 15.8 ounces, with a median close to this value and a standard deviation of 0.9 ounces, these figures suggest a tendency for bottles to contain slightly less than the labeled 16 ounces, although variability exists.

Constructing a 95% Confidence Interval

The next step involves calculating a 95% confidence interval for the true mean content of the bottles. This interval provides a range within which we expect the actual average bottle volume to fall with 95% certainty. Using the sample mean, standard deviation, and the t-distribution (due to the small sample size), the confidence interval offers a statistical basis to assess if the population mean differs significantly from 16 ounces. For instance, if the 95% CI ranges from 15.6 to 16.0 ounces, it indicates that the true mean could be less than the advertised amount, supporting potential underfilling issues.

Hypothesis Testing

The hypothesis test assesses the claim that bottles contain less than 16 ounces. The null hypothesis (H0) states that the mean volume is equal to 16 ounces, while the alternative hypothesis (H1) asserts that it is less than 16 ounces. This is a one-tailed test. Using the sample data, we calculate the test statistic:

t = (sample mean - hypothesized mean) / (sample standard deviation / sqrt(n))

Suppose the sample mean is 15.8 ounces, the standard deviation is 0.9 ounces, and n=30. The test statistic becomes t ≈ (15.8 - 16) / (0.9 / √30) ≈ -1.81. Comparing this t-value to the critical t-value at a 5% significance level for 29 degrees of freedom (approximately -1.699), since -1.81

Discussion Based on Conclusion

Given the statistical evidence supporting underfilling, it is essential to explore potential causes. Three possible reasons include:

1. Calibration errors in filling machinery: Inaccurate calibration could result in bottles being filled with less soda than intended.
2. Mechanical malfunctions or wear and tear: Over time, mechanical parts may degrade, leading to inconsistent filling volumes.
3. Inadequate quality control processes: Insufficient monitoring may allow underfilled bottles to reach consumers without correction.

To prevent future underfilling, strategies could include implementing routine machinery calibration checks, scheduling regular maintenance, and enhancing quality control protocols with real-time monitoring systems.

Alternatively, if the analysis had shown no significant evidence of underfilling, a different discussion would ensue. For example, customer perception issues or measurement inaccuracies might explain complaints, and strategies such as consumer education or calibration verification could be proposed.

Conclusion

This investigation using statistical methods indicates that the average volume in sampled bottles is less than 16 ounces, with significant confidence. Addressing the potential causes through improved calibration, maintenance, and quality assurance can help ensure compliance and maintain customer trust.

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