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 305.89 Newtons and 44.27 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. Assuming the population standard deviation is the same as the sample's, how many specimens must be tested to predict the breaking force to within 10 Newtons (about the weight of 1 liter or quart of water), at the 95% confidence level? Assuming the population standard deviation is the same as the sample's, how many specimens must be tested to predict the breaking force to within 1 Newton (the weight of an apple), at the 95% confidence level? Assuming that it costs money to test each specimen, why would a scientist choose to only test within 10 Newtons?

Explanation / Answer

A) 95% confidence interval = [xbar ± T critical *s/n]

= [305.89  ± 2.571 * 44.27/6]

= [259.424, 352.36]

B) Sample size, n = [Z critical *SD / margin error]2

= [1.96 * 44.27 / 10]2

= 76

C)

Sample size, n = [Z critical *SD / margin error]2

= [1.96 * 44.27 / 1]2

= 7529

D) Because, within 10 SD, sample size is 76. It is large enough sample number

but within 1 SD, sample size is 7529, it is very large sample and it is not required

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