An article in Knee Surgery Sports Traumatology Arthroscopy 2

An article in Knee Surgery, Sports Traumatology, Arthroscopy (2005, Vol. 13, pp. 273

An article in Knee Surgery, Sports Traumatology, Arthroscopy (2005, Vol. 13, pp. 273??279) ??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 95% two-sided confidence interval on the proportion of such tears that will heal. Round the answers to 3 decimal places.

Solution

(a) Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

So the lower bound is

p - Z*sqrt(p*(1-p)/n) = 0.676-1.96*sqrt(0.676*(1-0.676)/37) =0.525

So the upper bound is

p + Z*sqrt(p*(1-p)/n) = 0.676+1.96*sqrt(0.676*(1-0.676)/37) =0.827

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(b) Given a=0.05, Z(0.05) = 1.64 (from standard normal table)

So the lower bound is

p - Z*sqrt(p*(1-p)/n) = 0.676-1.64*sqrt(0.676*(1-0.676)/37) =0.550