A simple random sample of the 10000 elements in the populati

A simple random sample of the 10,000 elements in the population frame was obtained. Suppose the 75 indicated in the affirmative to the question posed to the sample. What is the sample size required to estimate the proportion of within a bound on the error of estimation with a magnitude of .02?

Solution

Usually, we use a 95% confidence level when it is not given. So, we use that here.

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Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.025  
       
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
E =    0.02  
p =    0.0075  
      
Thus,      
      
n =    71.48714774  
      
Rounding up,      
      
n =    72   [ANSWER]

If you want to get the sample size for another confidence level (other than 95%), please resubmit this question so we can help you! Thanks!