How many people should be surveyed using standard survey sta

How many people should be surveyed using standard survey standards to achieve a margin of error or +/- 2. +/- 3, and +/-4?

Solution

4. Note that we usually use 95% confidence, with no prior estimate.

a) For +/- 2%:

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 =    0.02  
p =    0.5  
      
Thus,      
      
n =    2400.911763  
      
Rounding up,      
      
n =    2401   [ANSWER]

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b) For +/- 3%:

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 =    0.03  
p =    0.5  
      
Thus,      
      
n =    1067.071895  
      
Rounding up,      
      
n =    1068   [ANSWER]

**************

c)

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 =    0.04  
p =    0.5  
      
Thus,      
      
n =    600.2279407  
      
Rounding up,      
      
n =    601   [ANSWER]