I am the manager at a major bottling company. Customers have begun to complain that the bottles of our brand of soda contains less than the advertised sixteen (16) ounces of product. My boss has asked me to investigate and solve the problem at hand. I have asked my employees to pull and measure the amount of soda in each of thirty (30) randomly selected bottles off the line from all the shifts at the bottling plant. 1. The following calculations show the mean, median and standard deviation for the case study.
The mean was calculated by getting the sum of total ounces in each bottle and then dividing that total by the sample size of thirty (30). Median = 14.8
The median is derived from the number that is in the middle, once the measurements have been placed in chronological order. Since the sample size is an even number, the median is obtained by taking the average of the two numbers in the middle.
Standard Deviation = 0.55033
The standard deviation is the square root of the variance, which is average of the squares of the distance that each value is from the mean. 2. 95% Confidence Interval = 6.056489716
The CI (confidence interval) is a specific interval estimate of parameter determined by using data obtained from a sample and the specific confidence level of the estimate.
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. Unfortunately, I was unable to complete this step in the investigation for lack of understanding and preparation. But, if I had to guess, I would say that the bottles do not contain the sixteen (16) ounces advertised. 4. Provide three (3) speculations as to why the bottles have less than sixteen (16) ounces of soda. The equipment was faulty in set up.
Purposely designed to have less than sixteen (16) ounces for the purpose of expansion because acidic products need to have room for built up pressure. If a bottle has been agitated in transportation, once it is opened, there will be an exploded release of pressure. The calibration on the machine needs to be reset.
In an effort to avoid the deficit in the future, the company can schedule frequent maintenance to the equipment to ensure proper function.