An73 Bn44 Cn72 Dn103 Find the minimum sample size when we wa

A)n=73

B)n=44

C)n=72

D)n=103

Find the minimum sample size when we want to construct a 90% confidence interval on the population proportion for the support of candidate A in the following mayoral election. Candidate A is facing two opposing candidates. In a preselected poll of 100 residents, 22 supported her. The desired margin of error is 0.08.

Solution

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.05  
       
      
Using a table/technology,      
      
z(alpha/2) =    1.644853627  
      
Also,      
      
E =    0.08  
p =    0.22  
      
Thus,      
      
n =    72.54238386  
      
Rounding up,      
      
n =    73   [ANSWER, A]