Bottling Company Case Study
Instructor: Agata Corobana
December 2, 2014
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.
A Confidence interval is a term used in inferential statistics that measures the probability that a population or sample parameter will be fall between two set values. The confidence interval can take any number of probabilities, with the most common being 95% or 99% (Investopedia.com, n.d.).
To find the 95% confidence interval for the ounces in the bottles, we need to find the margin of error E.
446.1 / 30 = 14.87
x̄ = 14.87 n= 30 σ = 0.5503
E = (14.87 + 14.87) / 2 = 14.8
The 95% confidence interval for the ounces in the bottles can be written as
x̄ ±E = 14.87- 0.2 and 14.87 + 0.2 = 14.67 ~ 15.07
In conclusion, with 95% confidence, the mean of the ounces in the bottles is between 14.67 ~ 15.07 ounces.
A statistical hypothesis is a statement about the distribution of the data variable X. Equivalently, a statistical hypothesis specifies a set of possible distributions of X (namely, the set of distributions for which the statement is true). In hypothesis testing, the goal is to see if there is sufficient statistical evidence to reject a presumed null hypothesis in favor of a conjectured alternative hypothesis. The null hypothesis is usually denoted H0 while the alternative hypothesis is usually denoted H1. A hypothesis that specifies a single distribution for X is called simple; a hypothesis that...