The technology underlying hip replacements has changed as these operations have

Question

The technology underlying hip replacements has changed as these operations have become more popular (over 250,000 in the United States in 2008). Starting in 2003, highly durable ceramic hips were marketed. Unfortunately, for too many patients the increased durability has been counterbalanced by an increased incidence of squeaking. An article reported that in one study of 147 individuals who received ceramic hips between 2003 and 2005, 13 of the hips developed squeaking. (a) Calculate a lower confidence bound at the 95% confidence level for the true proportion of such hips that develop squeaking. 0.043

Explanation / Answer

Let X be the random variable denoting the number of squeaking out of n(here 147) persons.

Therfore, X~Bin(147,p) where p is the true proportion of hips deloping squeaking.

Now, p_hat=x/n = 13/147=0.08843537

Expectation(p_hat)=E(X)/n=p

Variance(p_hat)=p(1-p)/n

So,lower confidence bound of p is = p_hat-(sqrt(variance(p_hat)))*z_a/2

where z_a/2 is the .975th alpha point of Standard Normal distribution=1.959964

Calculating the lower bound we get 0.05100904

Note:we have assumed Normal approximation as 147 is large.

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