An article in Knee Surgery sports traumatology Arthroscopy 2

An article in Knee Surgery, sports traumatology, Arthroscopy (2005, Vol. 13, pp. 273-279) considered arthroscopic meniscal repair with an absorbable screw. Results showed that for tears greater than 25 millimeters, 14 of 18 (78%) repairs were successful, but for shorter tears, 22 of 30 (73%) repairs were successful.

(a) Calculate a one-sided 95% confidence bound on the difference in proportions.

(b) Is there evidence that the success rate is greater for longer tears? Use signifcant level = 0:05. What is your conclusion?

Solution

a)

Formulating the hypotheses          
Ho: p1 - p2   <=   0  
Ha: p1 - p2   >   0  

Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.777777778      
p2 = x2/n2 =    0.733333333      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.126967371      
          
Thus,          
          
          
For the   95%   confidence level, then  
          
alpha = (1 - confidence level) =    0.05      
z(alpha) =    1.644853627      
          
lower bound = p1^ - p2^ - z(alpha/2) * sd =    -0.164398296      
  
          
Thus, the confidence interval is          
          
p > -0.164398296 [ANSWER]

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b)

As the lower bound is less than 0, then there is no significant evidence that the success rate is greater for longer tears at 0.05 level. [ANSWER]