Acrylic bone cement is sometimes used in hip and knee replacements to secure an artificial joint in place. The force required to break an acrylic bone cement bond was measured for six specimens, and the resulting mean and standard deviation were 306.11 newtons and 41.96 newtons, respectively. Assuming that it is reasonable to believe that breaking force has a distribution that is approximately normal, use a 95% confidence interval to estimate the mean breaking force for acrylic bone cement (in newtons). (Enter your answer using interval notation. Round your numerical values to three decimal places.)
Guide On Rating System
Vote
To estimate the mean breaking force for acrylic bone cement with a 95% confidence interval, we can use the formula:
CI = x ± (z * σ / sqrt(n))
where
CI = confidence interval
x = sample mean
z = z-score for the desired level of confidence (in this case, for a 95% confidence level, z = 1.96)
σ = population standard deviation (known in this case)
n = sample size
Given:
Sample mean (x) = 306.11 newtons
Standard deviation (σ) = 41.96 newtons
Sample size (n) = 6
Substituting these values into the formula, we get:
CI = 306.11 ± (1.96 * 41.96 / sqrt(6))
Calculating the expression inside the parentheses:
1.96 * 41.96 / sqrt(6) ≈ 37.20
Therefore, the 95% confidence interval for the mean breaking force of acrylic bone cement is:
CI = 306.11 ± 37.20
Rounded to three decimal places:
CI ≈ [268.91, 343.31] (in newtons)
Got a question with my answer?
Cheapmath.com is completely free!
Asking question is free.
Getting answers is free.
+99