In each case find the approximate sample size required to co

In each case, find the approximate sample size required to construct a 95% confidence interval for p that has a margin of error of ME = .08.

Assume p is near .2.

Assume you have no prior knowledge about p, but you wish to be certain that your sample is large enough to achieve the specified accuracy for the estimate.

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 =    0.08  
p =    0.2  
      
Thus,      
      
n =    96.03647052  
      
Rounding up,      
      
n =    97   [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 =    0.08  
p =    0.5  
      
Thus,      
      
n =    150.0569852  
      
Rounding up,      
      
n =    151   [ANSWER]