Question

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 percentage of cacao in its dark chocolate products, quality inspectors sample 25 pieces. They find a sample mean of​ 40% with a standard deviation of​ 8%. What is the​ 95% confidence interval for the true mean percentage of​ cacao?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 40%

sample standard deviation = s = 8%

sample size = n = 25

Degrees of freedom = df = n - 1 = 25 - 1 = 24

At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t0.025,24 = 2.064

Margin of error = E = t/2,df * (s /n)

= 2.064 * (8 / 25)

Margin of error = E = 3.30%

The 95% confidence interval estimate of the population mean is,

  ± E  

= 40%  ± 3.30%

= ( 36.70%, 43.30% )