To estimate the number of calories in a cup of diced chicken

To estimate the number of calories in a cup of diced chicken breast meat, the number of calories in a sample of four separate cups of meat is measured. The sample mean is 211.8 calories with sample standard deviation 0.9 calorie. Assuming the caloric content of all such chicken meat is normally distributed, construct a 95% confidence interval for the mean number of calories in one cup of meat.

Solution

Note that              
Margin of Error E = t(alpha/2) * s / sqrt(n)              
Lower Bound = X - t(alpha/2) * s / sqrt(n)              
Upper Bound = X + t(alpha/2) * s / sqrt(n)              
              
where              
alpha/2 = (1 - confidence level)/2 =    0.025          
X = sample mean =    211.8          
t(alpha/2) = critical t for the confidence interval =    3.182446305          
s = sample standard deviation =    0.9          
n = sample size =    4          
df = n - 1 =    3          
Thus,              
Margin of Error E =    1.432100837          
Lower bound =    210.3678992          
Upper bound =    213.2321008          
              
Thus, the confidence interval is              
              
(   210.3678992   ,   213.2321008   ) [ANSWER]