Arthroscopic meniscal repair with an absorbable screw result

Arthroscopic meniscal repair with an absorbable screw: results and surgical technique

Arthroscopic meniscal repair with an absorbable screw: results and surgical technique?? showed that only 25 out of 37 tears (67.6%) located between 3 and 6 mm from the meniscus rim were healed. (a) Calculate a 99% two-sided confidence interval on the proportion of such tears that will heal. Round the answers to 3 decimal places. ________________ leq p leq pleq_______________ (b)Calculate a 99% lower confidence bound on the proportion of such tears that will heal. Round the answer to 3 decimal places.

Solution

(a) Given a=1-0.99 = 0.01, Z(0.005) = 2.58 (from standard normal table)

So the lower bound is

p - Z*sqrt(p*(1-p)/n) = 0.676 - 2.58*sqrt(0.676*(1-0.676)/37) = 0.477

So the upper bound is

p+ Z*sqrt(p*(1-p)/n) =0.676 + 2.58*sqrt(0.676*(1-0.676)/37)=0.875

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(b) Given a=1-0.99=0.01, Z(0.01)=2.33 (from standard normal table)

So the lower bound is

p - Z*sqrt(p*(1-p)/n) = 0.676 - 2.33*sqrt(0.676*(1-0.676)/37) = 0.497