An Izod impact test was performed on 20 specimens of PVC pip

An Izod impact test was performed on 20 specimens of PVC pipe. The sample mean is x = 1.19 and the sample standard deviation is s = 0.23. Find a 99% lower confidence bound on the true Izod impact strength. Assume the data are normally distributed.

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Solution

Note that              
      
Lower Bound = X - t(alpha) * s / sqrt(n)                      
              
where  
          
alpha/2 = (1 - confidence level)/2 =    0.01          
X = sample mean =    1.19          
t(alpha/2) = critical t for the confidence interval =    2.539483191          
s = sample standard deviation =    0.23          
n = sample size =    20          
df = n - 1 =    19          
Thus,              

Lower bound =    1.059395488          

              
Thus, the confidence interval is              

1.059395488 <= u [answer]