Points 140 Assignment 1 Bottling Company Case Study Criteria

Points 140assignment 1 Bottling Company Case Studycriteriaunacceptab

Points 140 assignment 1: Bottling Company Case Study Criteria Unacceptable Below 60% F Meets Minimum Expectations 60-69% D Fair 70-79% C Proficient 80-89% B Exemplary 90-100% A 1. Calculate the mean, median, and standard deviation for ounces in the bottles. Weight: 20% Did not submit or incompletely calculated the mean, median, and standard deviation for ounces in the bottles. Insufficiently calculated the mean, median, and standard deviation for ounces in the bottles. Partially calculated the mean, median, and standard deviation for ounces in the bottles. Satisfactorily calculated the mean, median, and standard deviation for ounces in the bottles. Thoroughly calculated the mean, median, and standard deviation for ounces in the bottles. 2. Construct a 95% Confidence Interval for the ounces in the bottles. Weight: 25% Did not submit or incompletely constructed a 95% Confidence Interval for the ounces in the bottles. Insufficiently constructed a 95% Confidence Interval for the ounces in the bottles. Partially constructed a 95% Confidence Interval for the ounces in the bottles. Satisfactorily constructed a 95% Confidence Interval for the ounces in the bottles. Thoroughly constructed 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. Weight: 30% Did not submit or incompletely conducted a hypothesis test to verify if the claim that a bottle contains less than sixteen (16) ounces is supported. Did not submit or incompletely stated the logic of your test, the calculations, and the conclusion of your test. Insufficiently conducted a hypothesis test to verify if the claim that a bottle contains less than sixteen (16) ounces is supported. Insufficiently stated the logic of your test, the calculations, and the conclusion of your test. Partially conducted a hypothesis test to verify if the claim that a bottle contains less than sixteen (16) ounces is supported. Partially stated the logic of your test, the calculations, and the conclusion of your test. Satisfactorily conducted a hypothesis test to verify if the claim that a bottle contains less than sixteen (16) ounces is supported. Satisfactorily stated the logic of your test, the calculations, and the conclusion of your test. Thoroughly conducted a hypothesis test to verify if the claim that a bottle contains less than sixteen (16) ounces is supported. Thoroughly stated the logic of your test, the calculations, and the conclusion of your test. 4a. 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 4b. 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. Weight: 15% Did not submit or incompletely speculated on three (3) possible causes. Did not submit or incompletely suggested the strategies to avoid the deficit in the future. Or Did not submit or incompletely provided a detailed explanation to your boss about the situation. Did not submit or incompletely included your speculation on the reason(s) behind the claim, and did not submit or incompletely recommended one (1) strategy geared toward mitigating this issue in the future. Insufficiently speculated on three (3) possible causes. Insufficiently suggested the strategies to avoid the deficit in the future. Or Insufficiently provided a detailed explanation to your boss about the situation. Insufficiently included your speculation on the reason(s) behind the claim, and insufficiently recommended one (1) strategy geared toward mitigating this issue in the future. Partially speculated on three (3) possible causes. Partially suggested the strategies to avoid the deficit in the future. Or Partially provided a detailed explanation to your boss about the situation. Partially included your speculation on the reason(s) behind the claim, and partially recommended one (1) strategy geared toward mitigating this issue in the future. Satisfactorily speculated on three (3) possible causes. Satisfactorily suggested the strategies to avoid the deficit in the future. Or Satisfactorily provided a detailed explanation to your boss about the situation. Satisfactorily included your speculation on the reason(s) behind the claim, and satisfactorily recommended one (1) strategy geared toward mitigating this issue in the future. Thoroughly speculated on three (3) possible causes. Thoroughly suggested the strategies to avoid the deficit in the future. Or Thoroughly provided a detailed explanation to your boss about the situation. Thoroughly included your speculation on the reason(s) behind the claim, and thoroughly recommended one (1) strategy geared toward mitigating this issue in the future. 5. Writing / Support for ideas Weight: 5% Never uses reasons and evidence that logically support ideas. Rarely uses reasons and evidence that logically support ideas. Partially uses reasons and evidence that logically support ideas. Mostly uses reasons and evidence that logically support ideas. Consistently uses reasons and evidence that logically support ideas. 6. Writing / Grammar and mechanics Weight: 5% Serious and persistent errors in grammar, spelling, and punctuation. Numerous errors in grammar, spelling, and punctuation. Partially free of errors in grammar, spelling, and punctuation. Mostly free of errors in grammar, spelling, and punctuation. Free of errors in grammar, spelling, and punctuation.

Paper For Above instruction

The analysis of the bottling company's quality control data aims to investigate whether the bottles contain the advertised 16 ounces and to determine the reliability of the bottling process. This report employs statistical methods including descriptive statistics, confidence intervals, and hypothesis testing to assess the claim that bottles are less than 16 ounces.

1. Descriptive Statistics

The first step is to calculate the mean, median, and standard deviation of the ounces in the bottles. Assume sample data collected from the bottles provided the following measurements: 15.8, 15.9, 15.7, 15.6, 15.8, 15.9, 15.7, 15.8, 15.6, 15.9, 15.7, 15.8. Using this data, the mean is calculated by summing all measurements and dividing by the total number of observations. The median is found by ordering the data and selecting the middle value(s). The standard deviation measures the spread of the data points around the mean.

Calculations showed a mean of approximately 15.75 ounces, indicating that the average content per bottle is slightly less than the claimed 16 ounces. The median value similarly supports this conclusion. The standard deviation, calculated to be approximately 0.10 ounces, indicates low variability in the bottle sizes, suggesting consistent filling practices.

2. 95% Confidence Interval

Next, constructing a 95% confidence interval helps estimate the true mean size of all bottles in the process. Using the sample mean, standard deviation, and sample size, the confidence interval can be computed. For the given data, the interval ranges approximately from 15.68 to 15.82 ounces. This range does not include 16 ounces, providing statistical evidence that the average bottle contains less than the claimed amount with 95% confidence.

3. Hypothesis Test

The hypothesis test assesses if the evidence supports the claim that bottles contain less than 16 ounces. The null hypothesis (H0) states that the true mean is 16 ounces, while the alternative hypothesis (H1) suggests it is less than 16 ounces. Using a t-test due to sample size, the calculated t-statistic significantly exceeds the critical value at the 0.05 significance level, leading to the rejection of H0.

This statistical result supports the conclusion that bottles are, on average, less than 16 ounces, indicating a potential issue with the filling process.

4. Causes and Recommendations

4a. If the claim that bottles contain less than 16 ounces is supported:

Possible causes include calibration errors in the filling machines, deliberate under-filling to reduce costs, and operational inconsistencies such as machine wear or human error. To mitigate these issues, strategies include regular calibration of filling equipment, implementing stricter quality control checks, and providing employee training to ensure proper operation.

4b. If the claim is not supported:

If analysis suggests bottles are adequately filled, but the claim persists, possible reasons include measurement inaccuracies, customer perception issues, or external factors influencing consumer expectations. Strategies to address this include transparent communication about bottle content, quality assurance audits, and customer education to align expectations.

5. Importance of Documentation and Data Quality

Accurate data collection and thorough documentation are vital for making valid inferences from statistical analysis. Inconsistent or incomplete data could lead to erroneous conclusions, affecting decision-making processes. Therefore, implementing standardized data collection protocols is essential for reliable quality assessment.

6. Conclusion

Statistical analysis indicates that the bottles likely contain less than the advertised 16 ounces on average, primarily supported by the confidence interval and hypothesis testing results. The possible causes highlight operational issues that need attention to ensure product consistency and compliance. Adopting strategic improvements can enhance the manufacturing process, quality control, and customer satisfaction. Continued monitoring and proper statistical application will sustain process improvements and uphold product integrity.

References

• Montgomery, D. C., & Runger, G. C. (2014). Applied Statistics and Probability for Engineers. Wiley.
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