Assignment 1: Bottling Company Case Study
Assignment 1: Bottling Company Case Study
In this assignment, the application of statistics and probability theory to a real world business problem will be demonstrated. The task is to help a major bottling company to investigate the issue with customers’ claims. Many customers complained that the real amount of soda in the bottles produced by this company is less than advertised. The management of the company asked employees to collect the data of 30 randomly chosen bottles of soda. The data were recorded and given in the table below:
According to the advertisement of the company, each bottle contains 16 ounces of soda. The purpose of our analysis is to provide the appropriate descriptive statistics and verify if the customers’ claims about the amount soda in the bottles is supported. Start from descriptives – calculate mean, standard deviation and median for ounces in the bottles.
x=1nx1+x2+xn=15.854
The sample standard deviation is calculated by using the following formula:
s=1n-1i=1nxi-x2=0.661
The median is the 50th percentile of the data set. It is equal to 15.99
Construct the 95% confidence interval for the ounces in the bottles. The 95% confidence interval for population mean is calculated as follows:
x±1.96*sn15.854±1.96*0.66130
The lower 95% bound is 15.616, the upper 95% bound is 16.091. Hence, we are 95% confident that the true population average amount of ounces in the bottles produced by the company is between 15.616 and 16.091 ounces.
The final step of this assignment is to examine whether the sample mean of ounces is significantly less than 16 or not. We will use one-sample t-test for mean. Null hypothesis: the average amount of ounces in the bottles is not significantly different from 16. Alternative hypothesis: the average amount of ounces in the bottles is significantly less than 16.
H0: μ=16Ha: μ<16
Set the level of significance alpha at 5%.
Calculate t-statistics:
t=x-μsn=15.854-160.66130=-1.21
The critical value of one-tailed t-test is t(29, 0.05)=1.699.
Since the absolute value of t-observed is less than t-critical, we failed to reject the null hypothesis. There is no evidence to say that the average amount of soda in the bottles is significantly less than 16 ounces (at the 5% level of significance).
We have come to this conclusion based on a well-grounded statistical analysis. However, there is a real reason, why some customers began to complain about the difference in the advertised and the real amount of soda in the bottles. The problem is that the amount of soda varies significantly between the bottles. In a random sample of 30 bottles, there are bottles with the amount of soda from 14.23 to 16.96 ounces. The difference is more than 2.5 ounces and this is totally unacceptable. The management should pay attention on the process of filling bottles. There might be a problem with a filling machine. It may require some fixes so to improve the accuracy of filling.
