Good Example Of Case Study On Bottling Company Case Study

Bottling Company

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.

Calculate the Mean, Median, and Standard Deviation for Ounces in the Bottles.

According to Bluman, (2013), “the mean is calculated by summing up all the values given which is then divided by the total number of the observations or the total number of data values” (p. 114). According to the data of the bottling company given in the case, the mean ounces for the total of 30 observations will be 15.89 ounce. To calculate the median, first, the given set of data is arranged according to ascending or descending order then the midpoint of the data is found. The median of the data given in the case is 15.9. The standard deviation is the measure of variance. Lower the value standard deviation; more closer is the data towards the mean, while higher value of standard deviation indicates higher deviation of data set from the mean (Bluman, 2013). The standard deviation of the data given is 0.24.

Construct a 95% Confidence Interval For the Ounces in the Bottles.

The reliability or consistency of an estimate is measured by the confidence interval. Confidence interval is a range of value within which the value of an unknown parameter lies. Customers have begun to complain that the bottles of the brand of soda produced in the company contain less than the advertised sixteen (16) ounces of product. So, it is necessary to find the evidence so that we can conclude that the soda bottle have less than 16 ounce of soda. To calculate the 95% confidence interval, we will use formula as
Confidence interval = X ± Za/2 * σ/√(n)

Where,

X = mean =15.89
Za/2 = the confidence coefficient = 1.96
a = confidence level = 95% = 0.95
σ = standard deviation = 0.24
n = sample size = 30
Confidence interval = 15.89 ± 1.96 * 0.24/√30
Confidence interval = 15.89 ± 0.4597
So, the confidence interval is 15.13 to 16.3497.

Conduct a Hypothesis Test to Verify if Claim is Supported.

“Hypothesis testing is a decision-making process for evaluating claims about a population” (Bluman, 2013, p. 398). Hypothesis testing is done to justify whether or not the claim i.e. null hypothesis is to be accepted or rejected. According to the case, our null hypothesis and alternate hypothesis are:
Ho = Bottle contains 16 ounce soda.
H1 = Bottle contains less than 16 ounce of soda.
X= sample mean=15.89
μ= mean of population =16
s= Sample standard deviation = 0.24
n= sample size = 30

Then,

t = [x - μ] / [s / sqrt( n ) ]
t= [15.89 - 16] / [0.24 / sqrt( 30 ) ]
t =-0.11/0.23452
t = -0.469
The critical value of t statistics is 1.69912702. This shows that the null hypothesis is false. We can say that the bottle contains less than 16 ounce of soda.

Speculate on Three Possible Causes of Conclusion.

Out of several possibilities, the issue with the machine or the inefficiency of the machine could be the possible reason for this problem. There can have been miscalibration in the machine or we can say that the filling point of the machine could have some issues. The sensors at the filling zone might have been faulty leading to the case of filling the bottle less than 16 ounce. In addition to this, the human errors could be the possible reason. The person responsible could have taken out the bottles before they were filled completely. The next reason could be related to the physical properties of the soda. It might have been filled at higher temperature when the volume is higher. As the temperature falls, the volume of the liquid decreases. So, the temperature difference could have been another possible reason.

Suggest Strategies to Avoid the Deficit In the Future.

One best way to avoid the deficit is to run the sample test regularly. This will help the company to avoid the calibration errors in future. The machines must be regularly serviced and checked so that everything works fine. Higher emphasis must be given to quality control. Employees must be trained to match their performance according to the quality standards. Those employees must be made accountable for the errors made.

References

Bluman, A. G. (2013). Elementary statistics: A brief version (6th ed.). New York, NY: McGraw-
Hill.