Running head: BOTTLING COMPANY CASE STUDY 1

Bottling Company Case Study

BOTTLING COMPANY CASE STUDY 2
Abstract
In this assignment, I am a manager at a major bottling company and the customers have begun to make complaints that the bottles of the brand of soda produced at the company I work for have less than the advertised 16 ounces of soda. My boss wants me to solve the problem and has asked me to investigate into the situation. I have the employees on the floor pull 30 bottles off the line at random from every shift which I assume is from three shifts and I have asked the employees involved to measure the amount of soda there is in each of the 30 bottles.
The Mean, Median and Standard Deviation The mean or average of a data set is simply the average of all the numbers in the set. To find the average mean add up all the numbers in the data set and divide by how many numbers in the set. In this situation, there are 30 bottles with the weight of 14.5, 14.6, 14.7,14.8,14.9,15.3,14.9, 15.3, 14.9,15.5,14.8,15.2,15,15.1,15,14.4,15.8,14,16,16,15.8,14.5,14.1,14.2,14,14.9,14.7,14.5, 14.6,14.8, and 14.6. The total is 446.1 and divided by 30 and the mean is 14.87. The median is calculated by arranging the data in order and selecting the middle point and in this data set the median is an even number so we have to add the two middle numbers and divide by two which is 14.8 + 14.8/2 and the median is 14.8. The standard deviation is the sum of the values which is 0.545 rounded off to 0.55.
95% Confidence Interval To determine the critical value or “z” and because we want a 95% confidence interval the “z” is 1.96. With a mean score of 14.87 and a standard deviation of 0.55 and the desired confidence
BOTTLING COMPANY CASE STUDY 3 level of 95%, the confidence interval is +0.2. There is a 95% certainty that the true population mean falls within the range of 14.67 to 15.07. For calculating this, the mean is 14.87 and the standard deviation is 0.55. This means x=14.87, s=0.55 and n=30. Multiply 0.55 x 14.87 and divide by the square root of 30 which is 5.48. 1.96 x (0.55/5.48) =1.96 x 0.100= 0.196. The 95% confidence interval for the mean ounces of soda at this company is 14.87 plus or minus 0.196 ounces. The lower end of the interval is 14.87-0.196= 14.67; the upper end is 14.87 + 0.196= 15.07. So, it can be said that with a 95% confidence, that the average ounce of the bottles in the whole bottling company is between 14.67 ounces and 15.07 ounces based on the samples (Rumsey, 2003, p. 206).
Hypothesis Test There is a complaint that bottles of soda filled at the company contain less than 16 ounces of soda. In order to verify if the claim that a bottle contains less than 16 ounces is supported, the employees have pulled 30 bottles at random from all shifts and they have to measure the amount of soda in each bottle. The null hypothesis is that the bottles of soda filled do not contain less than the advertised 16 ounces. For this example, a random sampling of 30 bottles have an average of 14.87 ounces and a standard deviation of 0.55. To find the test statistic subtract 14.87-16=-1.13. Take 0.55 and divide by the square root of 30 which is 5.48 which equals 0.100 for the standard error. Divide -1.13 by 5.48 and that equals -0.2062 which is the test statistic. To start out working out the hypothesis, one has to state the hypothesis which is:
BOTTLING COMPANY CASE STUDY 4 * HO:u=30 Bottles are equal to 16 ounces in the population * H1:u not equal to 30 Bottles are not equal to 16 ounces in the population
The hypothesis is worked out in this form 14.87-16=-1.13 and divided by 0.55/square root of 30 which equals -1849.09. The hypothesis has a critical value of 2.045. I reject the null hypothesis since -1849.09 falls outside the non-critical region and there is not enough evidence to support the customers’ complaints that they are less than 16 ounces in each bottle (Bluman, 2013, p. 428).
Conclusion of Test I have concluded that the claim is not supported and what would be told to my boss about the situation is that more research needs to be done with more bottles because of inconclusive findings. The reasons for these complaints is that some consumers may want coupons for free drinks by claiming that there is not a full 16 ounces in the bottles. Another reason may be that some customers have designated themselves “brand managers” for a company and that they are rebelling against a company for producing something they see objectionable for whatever reason. Eric Anderson states “they’re such good customers that they now feel like they should be guiding the company and when the company makes mistakes in the eyes of the consumer, they want to correct them” (as cited in Buchanan, 2013, para. 5). Another reason could be the customers are wanting to bolster their presence and establish
BOTTLING COMPANY CASE STUDY 5 themselves as experts in the industry. Consumers who are wanting social status tend to point out negative characteristics of a company (Buchanan, 2013, para. 6). A quality plan must be put into place so that the company’s product is up to par. Identifying the company’s key processes are important to the business operations standards of measuring the quality of the product must be put into place. A quality management plan is of importance because it prevents and resolves errors. Some tools that can be put into place are cause-and-effect diagrams for determining the cause of problems and control charts to identify process changes over time. Other examples are quality control checklists, testing processes on statistical sampling on a regular basis (Davoren, 2013, para. 2-3).

References
Bluman, A.G. (2013). Elementary statistics: A step by step approach. Columbus, Ohio: McGraw Hill Education.
Buchanan, C. (2013, August 26). The ethics of online product reviews: customers lie, too. Retrieved on March 16, 2014, from http://www.convercent.com/company-ethicist/the- ethics-of-online-product-reviews-customers-lie-too/
Davoren, J. (2013, September 8). What are the standards elements of a quality management plan? Retrieved on March 16, 2014 , from http://www.ehow.com/info_12312280_standard- elements-quality-management-plan.html.
Rumsey, D. (2003). Statistics for Dummies. Hoboken, New Jersey: Wiley Publishing Inc.