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%.
What is the margin of error at 95% confidence?

Question

Quizplus · Accepted Answer

The margin of error at 95% confidence for a sample mean can be calculated using the formula: $ME = Z \times \frac{\sigma}{\sqrt{n}}$, where $Z$ is the Z-score corresponding to the desired confidence level (for 95% confidence, $Z = 1.96$), $\sigma$ is the standard deviation of the sample, and $n$ is the sample size. Plugging in the values: $ME = 1.96 \times \frac{4\%}{\sqrt{36}} = 1.96 \times \frac{4\%}{6} = 1.96 \times 0.67\% \approx 1.31\%$. The closest option to this calculated value is 1.36%, which accounts for rounding differences in the calculation process.

Grandma Gertrude's Chocolates, a Family Owned Business, Has an Opportunity