Amedical researcher wants to construct a 99% confidence interval for the proportion of knee replacement surgeries that result in complications. an article in the journal of bone and joint surgery suggested that approximately 8% of such operations result in complications. using this estimate, what sample size is needed so that the confidence interval will have a margin of error of 0.082 ?

 Sample size of 73  is needed so that the confidence interval will have a margin of error of 0.082

Step-by-step explanation:

The formula to calculate the margin of error for population proportion is given by :-

Given : The proportion of operations result in complications :

Significance level :

Critical value =      [By standard normal distribution table]

Margin of error : E= 0.082

Substitute all the value in the above formula, we get

Squaring both sides , we get

Hence, the required sample size = 73