Ever wondered how much force it takes to punch through a she

Ever wondered how much force it takes to punch through a sheetrock wall? MissBusters did a study by assuming the distribution was normal. They randomly selected 5 walls and found it took an average of 3.22 Newtons with a standard deviation of 0.81 Newtons to break through a standard sheetrock wall. What is the 99% confidence interval for the force needed to break through the wall?

Solution

Note that              
              
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 =    3.22          
t(alpha/2) = critical t for the confidence interval =    4.604094871          
s = sample standard deviation =    0.81          
n = sample size =    5          
df = n - 1 =    4          
Thus,              
              
Lower bound =    1.552198805          
Upper bound =    4.887801195          
              
Thus, the confidence interval is              
              
(   1.552198805   ,   4.887801195   ) [ANSWER]