A researcher wishes to estimate the percentage of adults who

A researcher wishes to estimate the percentage of adults who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be with in 5 percentage points with 95% confidence if:

a.) he uses a previous estimate of 34% .. n= (round to nearest integer)

b.) he does not use any prior estimates? n= (round to nearest integer)

Solution

a)

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 =    0.05  
p =    0.34  
      
Thus,      
      
n =    344.8093437  
      
Rounding up,      
      
n =    345   [answer]

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b)

Note that      
      
n = z(alpha/2)^2 p (1 - p) / E^2      
      
where      
      
alpha/2 =    0.025  
As there is no previous estimate for p, we set p = 0.5.      
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
E =    0.05  
p =    0.5  
      
Thus,      
      
n =    384.1458821  
      
Rounding up,      
      
n =    385   [answer]