*Instructions*

## Bottling Company Case Study

**Calculate the Mean, Median, and Standard Deviations for Ounces in the Bottles**

According to Bluman (2013), the mean is derived by adding the values in the data set and dividing this total by the number of values. In the data set provided, the total value of the ounces is 475.62 ounces while the total number of bottles sampled is 30. Therefore, the mean of the data set provided is 15.854.

The median is arrived at by arranging all the values in the data set in ascending order and then finding the mid-point. In this instance, the median of the data set is 15.98. The next step is to calculate the standard deviation. The S.D. is the square root of the variance in the data set. The measurement is used to demonstrate how much variance there is between the values and their average. A low standard deviation implies that the data tends towards the mean. A high SD shows that the data points are spread out over a large range of numbers. The standard deviation for the ounces in the bottles is 0.661.

**Construct a 95% confidence interval for the ounces in the bottles**

A confidence level demonstrates the reliability of an estimated measure. The customers of the bottling company have raised issue with the ounces provided in the bottles sold by the company. They claim that the ounces found in the bottles they consume are less than the ounces that the company advertises. A confidence level will help the company determine whether the bottles contain fewer ounces than intimated in the company’s advertisements. The 95% confidence interval will be ±0.24 while the range for the true population mean will be 15.62 to 16.09.

**Conduct a hypothesis test to verify if claim is supported**

Bluman (2013) argues that hypothesis testing is the process of evaluating claims about a population. The hypothesis in this case is that the bottles from the sample population contain less than 16 ounces. The null hypothesis states that all the bottles contain 16 ounces. The hypothesis testing will help the company determine if the customers’ allegations are true by analyzing the evidence provided.

The significance level is 0.05 and the method used to test the hypothesis is the Z score. The Z score is -1.21 and from this result, we can infer that the mean is lower than 16 ounces because the score is lower than the critical value.

**Speculate on the Probable causes of conclusion**

From the above results, we can conclude that the company is selling bottles that contain less than 16 ounces. There are several reasons why the bottles do not contain 16 ounces. There could be a problem with the machinery such as the time it takes to fill the bottle has been reduced. In such an instance, the machine is being plagued by calibration errors meaning that the time it should take to fill the bottle is reduced. It could also be a case of human error whereby a worker put in the wrong calibrations in the machine. The machine will only fill the bottle until the level that it has been instructed to.

The assembly line may also not be working right such that the bottles on the line move too fast effectively reducing the time taken to fill a bottle. The speed of the assembly line may not allow the machines to fill the bottles with exactly 16 ounces of liquid. It could imply that the calibrations of the machine used and the movement of the assembly line are not aligned causing there to be a discrepancy in the amount put in the bottles. There could also be a problem with the bottles themselves making them unable to fit 16 ounces of liquid.

**Strategies to avoid deficit in the future**

The company needs to create a quality control department mandated to ensure that the quality of the product is maintained. The department will be in charge of running accuracy tests on the bottles on a regular basis. Regular check-ups on the machine and the assembly line will correct any calibration errors that may be in place. Random sampling of the bottles on a regular basis will also help identify potential problems on the assembly line. Quality control will also require that the company trains its personnel, create and maintain quality benchmarks, and tests products for any statistically significant variations from the norm.

**References**

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