A researcher wishes to estimate the proportion of adults who

A researcher wishes to estimate the proportion of adults who have. High speed internet access. What size sample should be obtained if she wishes the estimate to be within 0.04 with 90% confidence if. A) she uses a previous. Estimate of 0.48? B) she does not use any prior estimates

Solution

a)

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 =    0.04  
p =    0.48  
      
Thus,      
      
n =    422.0647788  
      
Rounding up,      
      
n =    423   [ANSWER]

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Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.05  
As there is no previous estimate for p, we set p = 0.5.      
      
Using a table/technology,      
      
z(alpha/2) =    1.644853627  
      
Also,      
      
E =    0.04  
p =    0.5  
      
Thus,      
      
n =    422.7411647  
      
Rounding up,      
      
n =    423   [ANSWER]