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%.

Question

Quizplus · Accepted Answer

The 90% confidence interval is calculated using the formula: mean ± (z * (standard deviation / sqrt(n))). For a 90% confidence level, the z-score is approximately 1.645. Thus, the interval is 55% ± (1.645 * (4% / sqrt(36))), which results in 53.87% to 56.13%.

Find the Confidence Interval