A random sample of 9 chocolate energy bars of a certain bran

A random sample of 9 chocolate energy bars of a certain brand has, on average, 240 calories with a standard deviation of 12 calories. Construct a 99 Percentage confidence interval for the true mean calorie content of this brand of energy bar. Assume that the distribution of the calories is approximately normal.

Solution

9.

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 =    0.005          
X = sample mean =    240          
t(alpha/2) = critical t for the confidence interval =    3.355387331          
s = sample standard deviation =    12          
n = sample size =    9          
df = n - 1 =    8          
Thus,              
Margin of Error E =    13.42154933          
Lower bound =    226.5784507          
Upper bound =    253.4215493          
              
Thus, the confidence interval is              
              
(   226.5784507   ,   253.4215493   ) [ANSWER]