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.Past data
Indicate a standard deviation of 4%.If quality control inspectors wish to estimate the %
Cacao to within 1% of the true mean with 95% confidence, how many pieces of
Chocolate should they sample?
A)29
B)62
C)54
D)89
E)36

Question

Quizplus · Accepted Answer

The sample size needed can be calculated using the formula: n = (z-score)^2 * (standard deviation)^2 / (margin of error)^2. Given a 95% confidence level, the z-score will be 1.96. The standard deviation is given as 4%. We want to estimate the cacao content within 1% of the true mean, which is the margin of error. So, n = (1.96)^2 * (0.04)^2 / (0.01)^2 = 61.87, which rounds up to 62. Therefore, the quality control inspectors should sample 62 pieces of chocolate.

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