Assignment 1: Bottling Company Case Study
Professor: Dr. Gregory C. Wright
Principles of Finance
Bottling Company Case Study
|Ounces||Bottle Number||Ounces||Bottle Number||Ounces|
The Calculation of the Mean, Median, Standard Deviation and Sum
Confidence Intervals Constructed at 95%
- Mean: The element of mean is calculated by taking the total of all the ounce values and dividing the sum by the number of values. For the values included for this assignment, the mean is: 𝑥̅=15.854SUM = 475.62/N=30 =15.854
- MedianMD:This is determined by identifying the midpoint of the values. For the data provided for this assignment, the median is:MD=15.99
- Standard Deviation:Determining the standard deviation is a value that is utilized to determine how broadly the data set differs. Standard deviation calculations based on the data provided for this assignment is:SD =0.661
- Sum: The sum is for this case study is the total number of ounces in: Σ = 475.62
The mean sample of bottled sodas is:𝑥̅=15.854
There are a total of 30 samples to make up the sample size that are a part of the data, son=30
The standard deviation sample observed is:s= 0.661
The population standard deviation:σ =0.650
Population Variance:σ2= 0.423
As a part of this case study I will work to the 95% confidence level, the corresponding confidence interval is set at: +0.24
The lower limit utilizing the 95% confidence levels is: = 15.617
The upper limit of the 95% confidence level is: = 16.090
By utilizing a 95% confidence level interval, I can determine with 95% confidence that the level interval of 15.617 to 16.090 will make up the mean population. This outcome is based on a 30 bottle sample of sodas.
Testing of Hypothesis
Because I understand that every bottle of soda should contain at least 16 ounces of soda, the hypothesis are:
Null hypothesis: The soda bottles manufactured do not have less than the publicized (16) ounces of beverage product. H0: μ = 16
Alternative hypothesis: The soda bottles manufactured does have less than the publicized (16) ounces of beverage product. H1: μ ≠ 16
Margin of error E =(16.09-15.62) = 0.47 / 2 = 0.236
Calculations of Z-Static Written Out
Conclusion: The evidence is clear for the alternative hypothesis in comparison to the null hypothesis. Because the sample size is the sample size is at least 30 and I know the standard deviation of the population, I will go with the Z-Statistic.
Test Study Conclusion
Because the final test shows that there is less than the publicized 16 ounces of beverage product in each bottle of soda, I think that the probable cause could be the result of the rounding process. If the bottling company takes part in a rounding strategy to round up the ounces of beverage product in each bottle, it is highly likely that every label indicates there are exactly 16 ounces in each bottle. Another highly likely source could be flaws in the production process due to faulty equipment. If machines that are designed to input exactly 16 ounces of beverage product in each bottle slightly off by a fraction of an ounce, then that can explain the unfilled bottles. If the company’s quality control process does not include the regular inspections of machines and computer programs, miss filled bottles could be the direct outcome. Furthermore, soda beverage products tend to fizz up and expand during the bottling process.
If the soda settles after leaving the manufacturing process, this could explain why the unfilled bottles made it through quality control as being 16 ounces full. Lastly, the age and shelf life of a beverage soda product can also be a direct cause of unfilled bottles. Evaporation of the product is highly likely over time, or it could also be a direct result of being stored at high temperatures or in direct sunlight. The company can adopt strategies to avoid future deficits. For example, the company can take part in routine quality control checks to assure production workers, machines, equipment and any computer programs are consistently up to standard. The company could also check for flaws or inconsistencies in the beverage settling process that could be problematic in assuring precise product calculation. Lastly, the company can reprogram equipment to add a fraction of an ounce more to each 16 ounce bottle of soda to make up for any environmental evaporation of the product before it reaches consumers.
Bluman, A. G., & Bluman, A. G. (2007). Minitab manual to accompany Elementary statistics: A
step by step approach. New York, NY: McGraw-Hill. Melicher, Ronald W., Norton, E. A. (2013-10-21).
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