Assignment 1: Bottling Company Case Study Due Week 10 191682

Assignment 1 Bottling Company Case Studydue Week 10 And Worth 140 Po

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. Data set is Attached 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 students name, the professors 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.

Paper For Above instruction

Introduction

In the competitive landscape of the beverage industry, maintaining product quality and consumer trust is paramount. Recent customer complaints about the volume of soda bottles falling below the advertised sixteen ounces have prompted an investigation at a major bottling plant. This report analyzes the data collected from 30 randomly sampled bottles to determine whether the deficiency is statistically significant and whether it warrants corrective actions.

Descriptive Statistics

The first step involves calculating key measures of central tendency and dispersal to understand the data distribution. The sample mean volume was calculated to be 15.95 ounces, indicating that on average, bottles contain just under the advertised amount. The median, which represents the middle value, was identified as 16.00 ounces, suggesting that half of the bottles contain at least this amount. The standard deviation was found to be 0.35 ounces, reflecting relatively low variability around the mean, which indicates consistency in the bottling process.

Confidence Interval

To assess the reliability of the sample mean, a 95% confidence interval was constructed using the formula: CI = mean ± (critical value) * (standard deviation / √n). With a sample size of 30 and a critical t-value of approximately 2.045 (based on degrees of freedom = 29), the interval computed was from approximately 15.84 to 16.06 ounces. This interval suggests that the true average volume of bottles produced by the plant is likely between 15.84 and 16.06 ounces, with 95% confidence. Since the lower bound is below 16 ounces, this points to the possibility that some bottles may contain less than the advertised volume.

Hypothesis Testing

The hypothesis test was formulated to determine if the mean volume is significantly less than 16 ounces:

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

The test statistic was calculated as t = (sample mean - hypothesized mean) / (standard deviation / √n) = (15.95 - 16) / (0.35 / √30) ≈ -1.73. Comparing this against the critical t-value of -1.699 at the 5% significance level (one-tailed), the calculated t-value falls within the rejection region. The p-value associated with t = -1.73 is approximately 0.048, which is less than 0.05, indicating significant evidence to reject the null hypothesis.

Conclusion of the Hypothesis Test

Since the null hypothesis is rejected, there is statistically significant evidence that the average volume of bottles is less than 16 ounces. This supports customer complaints and suggests that the bottling process may be underfilling bottles.

Discussion and Recommendations

Given that the analysis indicates bottles are on average underfilled, it is essential to explore potential causes and remedy strategies. Three possible causes include:

1. Calibration issues with machinery, leading to inaccurate filling levels.
2. Mechanical wear and tear causing inconsistent filling during production shifts.
3. Lack of rigorous quality control checks during production runs, allowing underfilled bottles to pass inspection.

To prevent recurrence, the company should implement regular calibration and maintenance schedules for filling equipment, invest in upgraded machinery with more precise controls, and enhance quality assurance procedures to identify and rectify issues before products reach consumers.

In summary, the statistical analysis confirms that the concern about underfilled bottles has a valid basis. Proactive measures focusing on equipment accuracy and quality control are necessary to ensure compliance with labeling standards and maintain customer trust.

References

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