Acrylic bone cement is sometimes used in hip and knee replacements to fix an art

Question

Acrylic bone cement is sometimes used in hip and knee replacements to fix an artificial joint in place. The force required to break an acrylic bone cement bond was measured for six specimens under specified conditions, and the resulting mean and standard deviation were 302.19 Newtons and 44.17 Newtons, respectively. Assuming that it is reasonable to assume that breaking force under these conditions has a distribution that is approximately normal and using 95% confidence level, estimate the true average breaking force f for acrylic bone cement under the specified conditions. (Use Table 3 in Appendix A. Round your answer to the nearest whole number.) f

Explanation / Answer

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 =    302.19          
t(alpha/2) = critical t for the confidence interval =    2.570581836          
s = sample standard deviation =    44.17          
n = sample size =    6          
df = n - 1 =    5          
Thus,              
Margin of Error E =    46.35357221          
Lower bound =    255.8364278          
Upper bound =    348.5435722          
              
Thus, the confidence interval is              
              
(   255.8364278   ,   348.5435722   ) [ANSWER]

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