Find the Confidence Interval

question 6

Multiple Choice

Find the confidence interval.
-Grandma Gertrude's Chocolates, a family owned business, has an opportunity to
Supply its product for distribution through a large coffee house chain. However, the
Coffee house chain has certain specifications regarding cacao content as it wishes to
Advertise the health benefits (antioxidants) of the chocolate products it sells. In order to
Determine the mean % cacao in its dark chocolate products, quality inspectors sample 36
Pieces. They find a sample mean of 55% with a standard deviation of 4%.
The 90% confidence interval for the true mean % cacao is

• A) 53.87% to 56.13%.
• B) 51% to 59%.
• C) 53.33% to 56.67%.
• D) 53.64% to 56.36%
• E) 54.33% to 55.67%.

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Definitions:

Random Sample

A group of people selected from a bigger group, with every person having the same probability of being chosen.

Standard Deviation

A statistical tool that measures the extent of variation or scattering of values in a dataset, pointing out how much the data varies from the mean.

Normal Population

A statistical population that follows a normal distribution, characterized by its bell-shaped curve where most observations cluster around the central peak and the probabilities for values to occur are symmetrically distributed around the mean.

Mean Age

The average age calculated by adding all the ages together and dividing by the number of individuals.