California Wine producer Chill Wines has in their line a mid-market chardonnay, of which they produce 200,000 bottles a year. They have been bottling their wines with natural cork closures, which are known to have sealing issues resulting in the spoilage of wine, a problem that is worse in their chardonnay than in the other wines they sell. This problem, which results in a 15% spoilage rate for their chardonnay, is both expensive and impacts the company’s reputation.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 28EQ
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California Wine producer Chill Wines has in their line a mid-market chardonnay, of which
they produce 200,000 bottles a year. They have been bottling their wines with natural cork
closures, which are known to have sealing issues resulting in the spoilage of wine, a
problem that is worse in their chardonnay than in the other wines they sell. This problem,
which results in a 15% spoilage rate for their chardonnay, is both expensive and impacts
the company’s reputation. They have researched several other closure products on the
market and have decided to try using a new closure in a test run of 91 bottles their
chardonnay. After allowing the wine to stay in the bottles for the time it generally takes to
get it from the winery to customers, they tested the run and found 16 spoiled bottles. As the
company has a both an immediate financial and reputation risk, they want to be 90% sure
that changing the closures will help limit wine spoilage. What do their results suggest?

a)What is known? What information AND data does the problem provide?
Provide a bullet-pointed list with complete descriptions of what you know about the problem; include written
elements as well as numeric information.
b))What is unknown? What are you being asked to address? What is the problem that needs an
answer? You will not be describing a statistical outcome.
c))What are the data you are provided and what are their relevance in this statistical
problem? (i.e. sample, mean, population or other parameters. The two below at minimum must be precisely
described.)
What is the sample?
What is the population?

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